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General relativity: The expanding universe

By Pedro Ferreira

30 June 2010

The infant universe

(Image: NASA/WMAP Science Team)

One of general relativity’s most striking predictions arises if we consider what happens to the universe as a whole.

Shortly after Einstein published his theory, Russian meteorologist and mathematician Alexander Friedmann and Belgian priest Georges Lemaître showed that it predicted that the universe should evolve in response to all the energy it contains. They argued that the universe should start off small and dense, and expand and dilute with time. As a result, galaxies should drift away from each other.

Einstein was initially sceptical of Friedmann and Lemaître’s conclusion, favouring a static universe. But a discovery by the American astronomer Edwin Hubble changed his mind.

Hubble analysed how galaxies recede from the Milky Way. He found that distant galaxies move away faster than those that are relatively nearby. Hubble’s observations showed that the universe was indeed expanding. This model of the cosmos later became known as the big bang.

Over the past 20 years, a plethora of powerful observations by satellites and large telescopes have further firmed up the evidence for an expanding and evolving universe. We have obtained an accurate measure of the expansion rate of the universe and of the temperature of the “relic radiation” left over from the big bang, and we have been able to observe young galaxies when the universe was in its infancy. It is now accepted that the universe is about 13.7 billion years old.

Read more: Instant Expert: General relativity

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A widely held theory about the universe expanding has just been contradicted

New NASA data presents a challenge to a fundamental principle of cosmology.

Less than a second after the Big Bang , the universe suddenly blew up from nothing to a hot, dense sea of neutrons and electrons stretching across billions of lightyears.

And, 13.8 billion years later, the universe is still expanding, albeit at a much slower rate.

The prevailing theory, known as the isotropy hypothesis , argues that the universe is not only expanding but doing so at the same rate in all directions. But a new study suggests that may not be the case at all.

In a study published Wednesday in the journal Astronomy and Astrophysics, astronomers challenge this cornerstone theory of cosmology. The results suggest that while the universe is expanding, it is not expanding at the same rate in all directions.

The study relies on observations of some of the cosmos' largest structures, galaxy clusters , by three X-ray observatories: the European Space Agency’s XMM-Newton, NASA’s Chandra, and the German-led ROSAT.

The researchers looked at 800 galaxy clusters across the universe, measuring the temperature of each cluster's hot gas. They then compared the data with how bright the clusters appeared in the sky.

If the universe was in fact isotropic, then galaxy clusters of similar temperatures, located at similar distances, would have similar levels of luminosity. But that was not the case.

A map showing the rate of the expansion of the Universe in different directions across the sky.

Instead, the researchers noted significant differences.

“We saw that clusters with the same properties, with similar temperatures, appeared to be less bright than what we would expect in one direction of the sky, and brighter than expected in another direction,” Thomas Reiprich , professor at the University of Bonn, Germany and co-author of the new study, said in a statement .

“These differences are not random, but have a clear pattern depending on the direction in which we observed in the sky.”

Ultimately, the new study suggests that the universe is anisotropic , meaning that it has a different value when measured in different directions.

Dark forces — The scientists don't know what would cause the universe to expand at different rates in different places.

At first, they didn't entirely trust the results. They considered other explanations for the observations, including undetected gas, or dust blocking the view of the clusters. But the data did not support either of those scenarios.

Instead, they believe the weird observations may have something to do with dark energy .

Dark energy is a mysterious force that accounts for more than 60 percent of the universe, and accounts for the space in between cosmic bodies and holds matter in place through gravitational force.

Previous work suggests the universe is expanding at an accelerating rate. Scientists believe dark energy, which is essentially pulling galaxies apart, drives the acceleration.

Very little is known about dark energy, because it is impossible to observe. But scientists believe that it is not uniform. As a result, dark energy may be stronger in some parts of the universe, and weaker in other parts. If that is true, then it could cause the universe to expand at different rates in different places.

Universal consequences — The results, while odd, do not suggest the universe will run out of space in one direction faster than the other.

The universe does not need more ‘space’ to expand — its very expansion changes the metric of spacetime itself.

Different galaxy clusters reveal different properties across the universe.

The findings, however, may have a major impact on future astronomical observations.

“If the Universe is truly anisotropic, even if only in the past few billion years, that would mean a huge paradigm shift because the direction of every object would have to be taken into account when we analyze their properties,” Konstantinos Migkas , a graduate student at the University of Bonn and first author of the new study, said in the statement.

“Today, we estimate the distance of very distant objects in the Universe by applying a set of cosmological parameters and equations. We believe that these parameters are the same everywhere," he said.

"But if our conclusions are right then that would not be the case and we would have to revisit all our previous conclusions."

Abstract: The isotropy of the late Universe and consequently of the X-ray galaxy cluster scaling relations is an assumption greatly used in astronomy. However, within the last decade, many studies have reported deviations from isotropy when using various cosmological probes; a definitive conclusion has yet to be made. New, effective and independent methods to robustly test the cosmic isotropy are of crucial importance. In this work, we use such a method. Specifically, we investigate the directional behavior of the X-ray luminosity-temperature ( L X – T ) relation of galaxy clusters. A tight correlation is known to exist between the luminosity and temperature of the X-ray-emitting intracluster medium of galaxy clusters. While the measured luminosity depends on the underlying cosmology through the luminosity distance D L , the temperature can be determined without any cosmological assumptions. By exploiting this property and the homogeneous sky coverage of X-ray galaxy cluster samples, one can effectively test the isotropy of cosmological parameters over the full extragalactic sky, which is perfectly mirrored in the behavior of the normalization A of the L X – T relation. To do so, we used 313 homogeneously selected X-ray galaxy clusters from the Meta-Catalogue of X-ray detected Clusters of galaxies. We thoroughly performed additional cleaning in the measured parameters and obtain core-excised temperature measurements for all of the 313 clusters. The behavior of the L X – T relation heavily depends on the direction of the sky, which is consistent with previous studies. Strong anisotropies are detected at a ≳4 σ confidence level toward the Galactic coordinates ( l ,  b ) ∼ (280°, − 20°), which is roughly consistent with the results of other probes, such as Supernovae Ia. Several effects that could potentially explain these strong anisotropies were examined. Such effects are, for example, the X-ray absorption treatment, the effect of galaxy groups and low redshift clusters, core metallicities, and apparent correlations with other cluster properties, but none is able to explain the obtained results. Analyzing 10 5 bootstrap realizations confirms the large statistical significance of the anisotropic behavior of this sky region. Interestingly, the two cluster samples previously used in the literature for this test appear to have a similar behavior throughout the sky, while being fully independent of each other and of our sample. Combining all three samples results in 842 different galaxy clusters with luminosity and temperature measurements. Performing a joint analysis, the final anisotropy is further intensified (∼5 σ ), toward ( l ,  b ) ∼ (303°, − 27°), which is in very good agreement with other cosmological probes. The maximum variation of D L seems to be ∼16 ± 3% for different regions in the sky. This result demonstrates that X-ray studies that assume perfect isotropy in the properties of galaxy clusters and their scaling relations can produce strongly biased results whether the underlying reason is cosmological or related to X-rays. The identification of the exact nature of these anisotropies is therefore crucial for any statistical cluster physics or cosmology study.

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26.5: The Expanding Universe

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Learning Objectives

By the end of this section, you will be able to:

• Describe the discovery that galaxies getting farther apart as the universe evolves
• Explain how to use Hubble’s law to determine distances to remote galaxies
• Describe models for the nature of an expanding universe
• Explain the variation in Hubble’s constant

We now come to one of the most important discoveries ever made in astronomy—the fact that the universe is expanding. Before we describe how the discovery was made, we should point out that the first steps in the study of galaxies came at a time when the techniques of spectroscopy were also making great strides. Astronomers using large telescopes could record the spectrum of a faint star or galaxy on photographic plates, guiding their telescopes so they remained pointed to the same object for many hours and collected more light. The resulting spectra of galaxies contained a wealth of information about the composition of the galaxy and the velocities of these great star systems.

Slipher’s Pioneering Observations

Curiously, the discovery of the expansion of the universe began with the search for Martians and other solar systems. In 1894, the controversial (and wealthy) astronomer Percival Lowell established an observatory in Flagstaff, Arizona, to study the planets and search for life in the universe. Lowell thought that the spiral nebulae might be solar systems in the process of formation. He therefore asked one of the observatory’s young astronomers, Vesto M. Slipher (Figure \(\PageIndex{1}\)), to photograph the spectra of some of the spiral nebulae to see if their spectral lines might show chemical compositions like those expected for newly forming planets.

The Lowell Observatory’s major instrument was a 24-inch refracting telescope, which was not at all well suited to observations of faint spiral nebulae. With the technology available in those days, photographic plates had to be exposed for 20 to 40 hours to produce a good spectrum (in which the positions of the lines could reveal a galaxy’s motion). This often meant continuing to expose the same photograph over several nights. Beginning in 1912, and making heroic efforts over a period of about 20 years, Slipher managed to photograph the spectra of more than 40 of the spiral nebulae (which would all turn out to be galaxies).

To his surprise, the spectral lines of most galaxies showed an astounding redshift . By “redshift” we mean that the lines in the spectra are displaced toward longer wavelengths (toward the red end of the visible spectrum). Recall from the chapter on Radiation and Spectra that a redshift is seen when the source of the waves is moving away from us. Slipher’s observations showed that most spirals are racing away at huge speeds; the highest velocity he measured was 1800 kilometers per second.

Only a few spirals—such as the Andromeda and Triangulum Galaxies and M81—all of which are now known to be our close neighbors, turned out to be approaching us. All the other galaxies were moving away. Slipher first announced this discovery in 1914, years before Hubble showed that these objects were other galaxies and before anyone knew how far away they were. No one at the time quite knew what to make of this discovery.

Hubble’s Law

The profound implications of Slipher’s work became apparent only during the 1920s. Georges Lemaître was a Belgian priest and a trained astronomer. In 1927, he published a paper in French in an obscure Belgian journal in which he suggested that we live in an expanding universe. The title of the paper (translated into English) is “A Homogenous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae.” Lemaître had discovered that Einstein’s equations of relativity were consistent with an expanding universe (as had the Russian scientist Alexander Friedmann independently in 1922). Lemaître then went on to use Slipher’s data to support the hypothesis that the universe actually is expanding and to estimate the rate of expansion. Initially, scientists paid little attention to this paper, perhaps because the Belgian journal was not widely available.

In the meantime, Hubble was making observations of galaxies with the 2.5-meter telescope on Mt. Wilson, which was then the world’s largest. Hubble carried out the key observations in collaboration with a remarkable man, Milton Humason, who dropped out of school in the eighth grade and began his astronomical career by driving a mule train up the trail on Mount Wilson to the observatory (Figure \(\PageIndex{2}\)). In those early days, supplies had to be brought up that way; even astronomers hiked up to the mountaintop for their turns at the telescope. Humason became interested in the work of the astronomers and, after marrying the daughter of the observatory’s electrician, took a job as janitor there. After a time, he became a night assistant, helping the astronomers run the telescope and record data. Eventually, he made such a mark that he became a full astronomer at the observatory.

By the late 1920s, Humason was collaborating with Hubble by photographing the spectra of faint galaxies with the 2.5-meter telescope. (By then, there was no question that the spiral nebulae were in fact galaxies.) Hubble had found ways to improve the accuracy of the estimates of distances to spiral galaxies, and he was able to measure much fainter and more distant galaxies than Slipher could observe with his much-smaller telescope. When Hubble laid his own distance estimates next to measurements of the recession velocities (the speed with which the galaxies were moving away), he found something stunning: there was a relationship between distance and velocity for galaxies. The more distant the galaxy, the faster it was receding from us .

In 1931, Hubble and Humason jointly published the seminal paper where they compared distances and velocities of remote galaxies moving away from us at speeds as high as 20,000 kilometers per second and were able to show that the recession velocities of galaxies are directly proportional to their distances from us (Figure \(\PageIndex{3}\)), just as Lemaître had suggested.

We now know that this relationship holds for every galaxy except a few of the nearest ones. Nearly all of the galaxies that are approaching us turn out to be part of the Milky Way’s own group of galaxies, which have their own individual motions, just as birds flying in a group may fly in slightly different directions at slightly different speeds even though the entire flock travels through space together.

Written as a formula, the relationship between velocity and distance is

\[v=H \times d \nonumber\]

where \(v\) is the recession speed, \(d\) is the distance, and \(H\) is a number called the Hubble constant . This equation is now known as Hubble’s law .

Constants of Proportionality

Mathematical relationships such as Hubble’s law are pretty common in life. To take a simple example, suppose your college or university hires you to call rich alumni and ask for donations. You are paid $2.50 for each call; the more calls you can squeeze in between studying astronomy and other courses, the more money you take home. We can set up a formula that connects \(p\), your pay, and \(n\), the number of calls

\[p=A \times n \nonumber\]

where \(A\) is the alumni constant, with a value of $2.50. If you make 20 calls, you will earn $2.50 times 20, or $50.

Suppose your boss forgets to tell you what you will get paid for each call. You can calculate the alumni constant that governs your pay by keeping track of how many calls you make and noting your gross pay each week. If you make 100 calls the first week and are paid $250, you can deduce that the constant is $2.50 (in units of dollars per call). Hubble, of course, had no “boss” to tell him what his constant would be—he had to calculate its value from the measurements of distance and velocity.

Astronomers express the value of Hubble’s constant in units that relate to how they measure speed and velocity for galaxies. In this book, we will use kilometers per second per million light-years as that unit. For many years, estimates of the value of the Hubble constant have been in the range of 15 to 30 kilometers per second per million light-years The most recent work appears to be converging on a value near 22 kilometers per second per million light-years If \(H\) is 22 kilometers per second per million light-years, a galaxy moves away from us at a speed of 22 kilometers per second for every million light-years of its distance. As an example, a galaxy 100 million light-years away is moving away from us at a speed of 2200 kilometers per second.

Hubble’s law tells us something fundamental about the universe. Since all but the nearest galaxies appear to be in motion away from us, with the most distant ones moving the fastest, we must be living in an expanding universe. We will explore the implications of this idea shortly, as well as in the final chapters of this text. For now, we will just say that Hubble’s observation underlies all our theories about the origin and evolution of the universe.

Hubble’s Law and Distances

The regularity expressed in Hubble’s law has a built-in bonus: it gives us a new way to determine the distances to remote galaxies. First, we must reliably establish Hubble’s constant by measuring both the distance and the velocity of many galaxies in many directions to be sure Hubble’s law is truly a universal property of galaxies. But once we have calculated the value of this constant and are satisfied that it applies everywhere, much more of the universe opens up for distance determination. Basically, if we can obtain a spectrum of a galaxy, we can immediately tell how far away it is.

The procedure works like this. We use the spectrum to measure the speed with which the galaxy is moving away from us. If we then put this speed and the Hubble constant into Hubble’s law equation, we can solve for the distance.

Example \(\PageIndex{1}\): hubble's law

Hubble’s law (\(v = H \times d\)) allows us to calculate the distance to any galaxy. Here is how we use it in practice.

We have measured Hubble’s constant to be 22 km/s per million light-years. This means that if a galaxy is 1 million light-years farther away, it will move away 22 km/s faster. So, if we find a galaxy that is moving away at 18,000 km/s, what does Hubble’s law tells us about the distance to the galaxy?

\[d = \frac{v}{H} = \frac{18,000 \text{ km/s}}{ \frac{22 \text{ km/s}}{1 \text{ million light-years}}} = \frac{18,000}{22} \times \frac{1 \text{ million light-years}{1} = 818 \text{ million light-years} \nonumber\]

Note how we handled the units here: the km/s in the numerator and denominator cancel, and the factor of million light-years in the denominator of the constant must be divided correctly before we get our distance of 818 million light-years.

Exercise \(\PageIndex{1}\)

Using 22 km/s/million light-years for Hubble’s constant, what recessional velocity do we expect to find if we observe a galaxy at 500 million light-years?

\[v=d \times H = 500 \text{ million light-years} \times \frac{22 \text{ km/s}}{1 \text{ million light-years}} = 11,000 \text{ km/s} \nonumber\]

Variation of Hubble’s Constant

The use of redshift is potentially a very important technique for determining distances because as we have seen, most of our methods for determining galaxy distances are limited to approximately the nearest few hundred million light-years (and they have large uncertainties at these distances). The use of Hubble’s law as a distance indicator requires only a spectrum of a galaxy and a measurement of the Doppler shift, and with large telescopes and modern spectrographs, spectra can be taken of extremely faint galaxies.

But, as is often the case in science, things are not so simple. This technique works if, and only if, the Hubble constant has been truly constant throughout the entire life of the universe. When we observe galaxies billions of light-years away, we are seeing them as they were billions of years ago. What if the Hubble “constant” was different billions of years ago? Before 1998, astronomers thought that, although the universe is expanding, the expansion should be slowing down, or decelerating, because the overall gravitational pull of all matter in the universe would have a dominant, measureable effect. If the expansion is decelerating, then the Hubble constant should be decreasing over time.

The discovery that type Ia supernovae are standard bulbs gave astronomers the tool they needed to observe extremely distant galaxies and measure the rate of expansion billions of years ago. The results were completely unexpected. It turns out that the expansion of the universe is accelerating over time! What makes this result so astounding is that there is no way that existing physical theories can account for this observation. While a decelerating universe could easily be explained by gravity, there was no force or property in the universe known to astronomers that could account for the acceleration. In The Big Bang chapter, we will look in more detail at the observations that led to this totally unexpected result and explore its implications for the ultimate fate of the universe.

In any case, if the Hubble constant is not really a constant when we look over large spans of space and time, then the calculation of galaxy distances using the Hubble constant won’t be accurate. As we shall see in the chapter on The Big Bang, the accurate calculation of distances requires a model for how the Hubble constant has changed over time. The farther away a galaxy is (and the longer ago we are seeing it), the more important it is to include the effects of the change in the Hubble constant. For galaxies within a few billion light-years, however, the assumption that the Hubble constant is indeed constant gives good estimates of distance.

Models for an Expanding Universe

At first, thinking about Hubble’s law and being a fan of the work of Copernicus and Harlow Shapley, you might be shocked. Are all the galaxies really moving away from us ? Is there, after all, something special about our position in the universe? Worry not; the fact that galaxies are receding from us and that more distant galaxies are moving away more rapidly than nearby ones shows only that the universe is expanding uniformly.

A uniformly expanding universe is one that is expanding at the same rate everywhere. In such a universe, we and all other observers, no matter where they are located, must observe a proportionality between the velocities and distances of equivalently remote galaxies. (Here, we are ignoring the fact that the Hubble constant is not constant over all time, but if at any given time in the evolution of the universe the Hubble constant has the same value everywhere, this argument still works.)

To see why, first imagine a ruler made of stretchable rubber, with the usual lines marked off at each centimeter. Now suppose someone with strong arms grabs each end of the ruler and slowly stretches it so that, say, it doubles in length in 1 minute (Figure \(\PageIndex{4}\)). Consider an intelligent ant sitting on the mark at 2 centimeters—a point that is not at either end nor in the middle of the ruler. He measures how fast other ants, sitting at the 4-, 7-, and 12-centimeter marks, move away from him as the ruler stretches.

The ant at 4 centimeters, originally 2 centimeters away from our ant, has doubled its distance in 1 minute; it therefore moved away at a speed of 2 centimeters per minute. The ant at the 7-centimeters mark, which was originally 5 centimeters away from our ant, is now 10 centimeters away; it thus had to move at 5 centimeters per minute. The one that started at the 12-centimeters mark, which was 10 centimeters away from the ant doing the counting, is now 20 centimeters away, meaning it must have raced away at a speed of 10 centimeters per minute. Ants at different distances move away at different speeds, and their speeds are proportional to their distances (just as Hubble’s law indicates for galaxies). Yet, notice in our example that all the ruler was doing was stretching uniformly. Also, notice that none of the ants were actually moving of their own accord, it was the stretching of the ruler that moved them apart.

Now let’s repeat the analysis, but put the intelligent ant on some other mark—say, on 7 or 12 centimeters. We discover that, as long as the ruler stretches uniformly, this ant also finds every other ant moving away at a speed proportional to its distance. In other words, the kind of relationship expressed by Hubble’s law can be explained by a uniform stretching of the “world” of the ants. And all the ants in our simple diagram will see the other ants moving away from them as the ruler stretches.

For a three-dimensional analogy, let’s look at the loaf of raisin bread in Figure \(\PageIndex{5}\). The chef has accidentally put too much yeast in the dough, and when she sets the bread out to rise, it doubles in size during the next hour, causing all the raisins to move farther apart. On the figure, we again pick a representative raisin (that is not at the edge or the center of the loaf) and show the distances from it to several others in the figure (before and after the loaf expands).

Measure the increases in distance and calculate the speeds for yourself on the raisin bread, just like we did for the ruler. You will see that, since each distance doubles during the hour, each raisin moves away from our selected raisin at a speed proportional to its distance. The same is true no matter which raisin you start with.

Our two analogies are useful for clarifying our thinking, but you must not take them literally. On both the ruler and the raisin bread, there are points that are at the end or edge. You can use these to pinpoint the middle of the ruler and the loaf. While our models of the universe have some resemblance to the properties of the ruler and the loaf, the universe has no boundaries, no edges, and no center (all mind-boggling ideas that we will discuss in a later chapter).

What is useful to notice about both the ants and the raisins is that they themselves did not “cause” their motion. It isn’t as if the raisins decided to take a trip away from each other and then hopped on a hoverboard to get away. No, in both our analogies, it was the stretching of the medium (the ruler or the bread) that moved the ants or the raisins farther apart. In the same way, we will see in The Big Bang chapter that the galaxies don’t have rocket motors propelling them away from each other. Instead, they are passive participants in the expansion of space . As space stretches, the galaxies are carried farther and farther apart much as the ants and the raisins were. (If this notion of the “stretching” of space surprises or bothers you, now would be a good time to review the information about spacetime in Black Holes and Curved Spacetime. We will discuss these ideas further as our discussion broadens from galaxies to the whole universe.)

The expansion of the universe, by the way, does not imply that the individual galaxies and clusters of galaxies themselves are expanding. Neither raisins nor the ants in our analogy grow in size as the loaf expands. Similarly, gravity holds galaxies and clusters of galaxies together, and they get farther away from each other—without themselves changing in size—as the universe expands.

The universe is expanding. Observations show that the spectral lines of distant galaxies are redshifted, and that their recession velocities are proportional to their distances from us, a relationship known as Hubble’s law. The rate of recession, called the Hubble constant, is approximately 22 kilometers per second per million light-years. We are not at the center of this expansion: an observer in any other galaxy would see the same pattern of expansion that we do. The expansion described by Hubble’s law is best understood as a stretching of space.

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March 10, 2020

Solved: The mystery of the expansion of the universe

by University of Geneva

The Earth, solar system, the entire Milky Way and the few thousand galaxies closest to us move in a vast "bubble" that is 250 million light years in diameter, where the average density of matter is half as high as for the rest of the universe. This is the hypothesis advanced by a theoretical physicist from the University of Geneva (UNIGE) to solve a conundrum that has been splitting the scientific community for a decade: At what speed is the universe expanding? Until now, at least two independent calculation methods have arrived at two values that are different by about 10% with a deviation that is statistically irreconcilable. This new approach, which is set out in the journal Physics Letters B , erases this divergence without making use of any "new physics."

The universe has been expanding since the Big Bang occurred 13.8 billion years ago—a proposition first made by the Belgian canon and physicist Georges Lemaître (1894-1966), and first demonstrated by Edwin Hubble (1889-1953). The American astronomer discovered in 1929 that every galaxy is pulling away from us, and that the most distant galaxies are moving the most quickly. This suggests that there was a time in the past when all the galaxies were located at the same spot, a time that can only correspond to the Big Bang. This research gave rise to the Hubble-Lemaître law, including the Hubble constant (H0), which denotes the universe's rate of expansion. The best H0 estimates currently lie around 70 (km/s)/Mpc (meaning that the universe is expanding 70 kilometers a second more quickly every 3.26 million light years). The problem is that there are two conflicting methods of calculation.

Sporadic supernovae

The first is based on the cosmic microwave background: This is the microwave radiation that comes at us from everywhere, emitted at the time the universe became cold enough for light to be able to circulate freely (about 370,000 years after the Big Bang). Using the precise data supplied by the Planck space mission, and given the fact that the universe is homogeneous and isotropic, a value of 67.4 is obtained for H0 using Einstein's theory of general relativity to run through the scenario. The second calculation method is based on the supernovae that appear sporadically in distant galaxies . These very bright events provide the observer with highly precise distances, an approach that has made it possible to determine a value for H0 of 74.

Lucas Lombriser, a professor in the Theoretical Physics Department in UNIGE's Faculty of Sciences, explains: "These two values carried on becoming more precise for many years while remaining different from each other. It didn't take much to spark a scientific controversy and even to arouse the exciting hope that we were perhaps dealing with a 'new physics.'" To narrow the gap, professor Lombriser entertained the idea that the universe is not as homogeneous as claimed, a hypothesis that may seem obvious on relatively modest scales. There is no doubt that matter is distributed differently inside a galaxy than outside one. It is more difficult, however, to imagine fluctuations in the average density of matter calculated on volumes thousands of times larger than a galaxy.

The "Hubble Bubble"

"If we were in a kind of gigantic 'bubble,'" continues professor Lombriser, "where the density of matter was significantly lower than the known density for the entire universe, it would have consequences on the distances of supernovae and, ultimately, on determining H0."

All that would be needed would be for this "Hubble bubble" to be large enough to include the galaxy that serves as a reference for measuring distances. By establishing a diameter of 250 million light years for this bubble, the physicist calculated that if the density of matter inside was 50% lower than for the rest of the universe, a new value would be obtained for the Hubble constant, which would then agree with the one obtained using the cosmic microwave background . "The probability that there is such a fluctuation on this scale is one in 20 to one in 5, which means that it is not a theoretician's fantasy. There are a lot of regions like ours in the vast universe," says professor Lombriser

Journal information: Physics Letters B

Provided by University of Geneva

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On the Accelerated Expansion of the Universe

• Published: 04 April 2024
• Volume 30 , pages 85–88, ( 2024 )

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• Naman Kumar 1  

If we look from a quantum perspective, the most natural way in which the universe can be created is in entangled pairs whose time flow is oppositely related. This suggests the idea of the creation of a universe-antiuniverse pair. Assuming the validity of this hypothesis, in this paper, we show that the universe expands in an accelerated manner. The same reasoning holds for the anti-universe as well. This idea does not require any form of dark energy as used in the standard cosmological model \(\Lambda\) CDM or in modified theories of gravity.

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ACKNOWLEDGMENTS

We would like to thank the anonymous referee whose comments greatly improved the clarity of the manuscript.

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Kumar, N. On the Accelerated Expansion of the Universe. Gravit. Cosmol. 30 , 85–88 (2024). https://doi.org/10.1134/S0202289324010080

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Received : 06 June 2023

Revised : 23 September 2023

Accepted : 07 October 2023

Published : 04 April 2024

Issue Date : March 2024

DOI : https://doi.org/10.1134/S0202289324010080

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What is Dark Energy? Inside our accelerating, expanding Universe

Some 13.8 billion years ago, the universe began with a rapid expansion we call the big bang. After this initial expansion, which lasted a fraction of a second, gravity started to slow the universe down. But the cosmos wouldn’t stay this way. Nine billion years after the universe began, its expansion started to speed up, driven by an unknown force that scientists have named dark energy .

But what exactly is dark energy?

The short answer is: We don't know. But we do know that it exists, it’s making the universe expand at an accelerating rate, and approximately 68.3 to 70% of the universe is dark energy.

A Brief History

It all started with cepheids.

Dark energy wasn't discovered until the late 1990s. But its origin in scientific study stretches all the way back to 1912 when American astronomer Henrietta Swan Leavitt made an important discovery using Cepheid variables, a class of stars whose brightness fluctuates with a regularity that depends on the star's brightness.

All Cepheid stars with a certain period (a Cepheid’s period is the time it takes to go from bright, to dim, and bright again) have the same absolute magnitude, or luminosity – the amount of light they put out. Leavitt measured these stars and proved that there is a relationship between their regular period of brightness and luminosity. Leavitt’s findings made it possible for astronomers to use a star’s period and luminosity to measure the distances between us and Cepheid stars in far-off galaxies (and our own Milky Way).

Around this same time in history, astronomer Vesto Slipher observed spiral galaxies using his telescope’s spectrograph, a device that splits light into the colors that make it up, much like the way a prism splits light into a rainbow. He used the spectrograph, a relatively recent invention at the time, to see the different wavelengths of light coming from the galaxies in different spectral lines. With his observations, Silpher was the first astronomer to observe how quickly the galaxy was moving away from us, called redshift, in distant galaxies. These observations would prove to be critical for many future scientific breakthroughs, including the discovery of dark energy.

Redshift is a term used when astronomical objects are moving away from us and the light coming from those objects stretches out. Light behaves like a wave, and red light has the longest wavelength. So, the light coming from objects moving away from us has a longer wavelength, stretching to the “red end” of the electromagnetic.

Discovering an Expanding Universe

The discovery of galactic redshift, the period-luminosity relation of Cepheid variables, and a newfound ability to gauge a star or galaxy’s distance eventually played a role in astronomers observing that galaxies were getting farther away from us over time, which showed how the universe was expanding. In the years that followed, different scientists around the world started to put the pieces of an expanding universe together.

In 1922, Russian scientist and mathematician Alexander Friedmann published a paper detailing multiple possibilities for the history of the universe. The paper, which was based on Albert Einstein’s theory of general relativity published in 1917, included the possibility that the universe is expanding.

In 1927, Belgian astronomer Georges Lemaître, who is said to have been unaware of Friedmann’s work, published a paper also factoring in Einstein’s theory of general relativity. And, while Einstein stated in his theory that the universe was static, Lemaître showed how the equations in Einstein’s theory actually support the idea that the universe is not static but, in fact, is actually expanding.

Astronomer Edwin Hubble confirmed that the universe was expanding in 1929 using observations made by his associate, astronomer Milton Humason. Humason measured the redshift of spiral galaxies. Hubble and Humason then studied Cepheid stars in those galaxies, using the stars to determine the distance of their galaxies (or nebulae, as they called them). They compared the distances of these galaxies to their redshift and tracked how the farther away an object is, the bigger its redshift and the faster it is moving away from us. The pair found that objects like galaxies are moving away from Earth faster the farther away they are, at upwards of hundreds of thousands of miles per second – an observation now known as Hubble’s Law, or the Hubble-Lemaître law. The universe, they confirmed, is really expanding.

Expansion is Speeding Up, Supernovae Show

Scientists previously thought that the universe's expansion would likely be slowed down by gravity over time, an expectation backed by Einstein's theory of general relativity. But in 1998, everything changed when two different teams of astronomers observing far-off supernovae noticed that (at a certain redshift) the stellar explosions were dimmer than expected. These groups were led by astronomers Adam Riess, Saul Perlmutter, and Brian Schmidt. This trio won the 2011 Nobel Prize in Physics for this work.

While dim supernovae might not seem like a major find, these astronomers were looking at Type 1a supernovae , which are known to have a certain level of luminosity. So they knew that there must be another factor making these objects appear dimmer. Scientists can determine distance (and speed) using an objects' brightness, and dimmer objects are typically farther away (though surrounding dust and other factors can cause an object to dim).

This led the scientists to conclude that these supernovae were just much farther away than they expected by looking at their redshifts.

Using the objects’ brightness, the researchers determined the distance of these supernovae. And using the spectrum, they were able to figure out the objects’ redshift and, therefore, how fast they were moving away from us. They found that the supernovae were not as close as expected, meaning they had traveled farther away from us faster than ancitipated. These observations led scientists to ultimately conclude that the universe itself must be expanding faster over time.

While other possible explanations for these observations have been explored, astronomers studying even more distant supernovae or other cosmic phenomena in more recent years continued to gather evidence and build support for the idea that the universe is expanding faster over time, a phenomenon now called cosmic acceleration. 

But, as scientists built up a case for cosmic acceleration, they also asked: Why? What could be driving the universe to stretch out faster over time?

Enter dark energy.

What Exactly is Dark Energy?

Right now, dark energy is just the name that astronomers gave to the mysterious "something" that is causing the universe to expand at an accelerated rate.

Dark energy has been described by some as having the effect of a negative pressure that is pushing space outward. However, we don't know if dark energy has the effect of any type of force at all. There are many ideas floating around about what dark energy could possibly be. Here are four leading explanations for dark energy. Keep in mind that it's possible it's something else entirely.

Vacuum Energy:

Some scientists think that dark energy is a fundamental, ever-present background energy in space known as vacuum energy, which could be equal to the cosmological constant, a mathematical term in the equations of Einstein's theory of general relativity. Originally, the constant existed to counterbalance gravity, resulting in a static universe. But when Hubble confirmed that the universe was actually expanding, Einstein removed the constant, calling it “my biggest blunder,” according to physicist George Gamow.

But when it was later discovered that the universe’s expansion was actually accelerating, some scientists suggested that there might actually be a non-zero value to the previously-discredited cosmological constant. They suggested that this additional force would be necessary to accelerate the expansion of the universe. This theorized that this mystery component could be attributed to something called “vacuum energy,” which is a theoretical background energy permeating all of space.

Space is never exactly empty. According to quantum field theory, there are virtual particles, or pairs of particles and antiparticles. It's thought that these virtual particles cancel each other out almost as soon as they crop up in the universe, and that this act of popping in and out of existence could be made possible by “vacuum energy” that fills the cosmos and pushes space outward.

While this theory has been a popular topic of discussion, scientists investigating this option have calculated how much vacuum energy there should theoretically be in space. They showed that there should either be so much vacuum energy that, at the very beginning, the universe would have expanded outwards so quickly and with so much force that no stars or galaxies could have formed, or… there should be absolutely none. This means that the amount of vacuum energy in the cosmos must be much smaller than it is in these predictions. However, this discrepancy has yet to be solved and has even earned the moniker "the cosmological constant problem."

Quintessence:

Some scientists think that dark energy could be a type of energy fluid or field that fills space, behaves in an opposite way to normal matter, and can vary in its amount and distribution throughout both time and space. This hypothesized version of dark energy has been nicknamed quintessence after the theoretical fifth element discussed by ancient Greek philosophers.

It's even been suggested by some scientists that quintessence could be some combination of dark energy and dark matter, though the two are currently considered completely separate from one another. While the two are both major mysteries to scientists, dark matter is thought to make up about 85% of all matter in the universe.

Space Wrinkles:

Some scientists think that dark energy could be a sort of defect in the fabric of the universe itself; defects like cosmic strings, which are hypothetical one-dimensional "wrinkles" thought to have formed in the early universe. 

A Flaw in General Relativity:

Some scientists think that dark energy isn't something physical that we can discover. Rather, they think there could be an issue with general relativity and Einstein's theory of gravity and how it works on the scale of the observable universe. Within this explanation, scientists think that it's possible to modify our understanding of gravity in a way that explains observations of the universe made without the need for dark energy. Einstein actually proposed such an idea in 1919 called unimodular gravity, a modified version of general relativity that scientists today think wouldn't require dark energy to make sense of the universe.

Dark energy is one of the great mysteries of the universe. For decades, scientists have theorized about our expanding universe. Now, for the first time ever, we have tools powerful enough to put these theories to the test and really investigate the big question: “what is dark energy?”

NASA plays a critical role in the ESA (European Space Agency) mission Euclid (launched in 2023), which will make a 3D map of the universe to see how matter has been pulled apart by dark energy over time. This map will include observations of billions of galaxies found up to 10 billion light-years from Earth.

NASA's Nancy Grace Roman Space Telescope , set to launch by May 2027, is designed to investigate dark energy, among many other science topics, and will also create a 3D dark matter map. Roman's resolution will be as sharp as NASA’s Hubble Space Telescope's, but with a field of view 100 times larger, allowing it to capture more expansive images of the universe. This will allow scientists to map how matter is structured and spread across the universe and explore how dark energy behaves and has changed over time. Roman will also conduct an additional survey to detect Type Ia supernovae

In addition to NASA’s missions and efforts, the Vera C. Rubin Observatory, supported by a large collaboration that includes the U.S. National Science Foundation, which is currently under construction in Chile, is also poised to support our growing understanding of dark energy. The ground-based observatory is expected to be operational in 2025.

The combined efforts of Euclid, Roman, and Rubin will usher in a new “golden age” of cosmology, in which scientists will collect more detailed information than ever about the great mysteries of dark energy.

Additionally, NASA's James Webb Space Telescope (launched in 2021), the world’s most powerful and largest space telescope, aims to make contributions to several areas of research, and will contribute to studies of dark energy.

NASA's SPHEREx (the Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer) mission, scheduled to launch no later than April 2025, aims to investigate the origins of the universe. Scientists expect that the data collected with SPHEREx, which will survey the entire sky in near-infrared light, including over 450 million galaxies, could help to further our understanding of dark energy.

NASA also supports a citizen science project called Dark Energy Explorers , which enables anyone in the world, even those who have no scientific training, to help in the search for dark energy answers.

*A brief note*

Lastly, to clarify, dark energy is not the same as dark matter. Their main similarity is that we don't yet know what they are!

By Chelsea Gohd NASA's Jet Propulsion Laboratory

Related Terms

• Dark Energy
• Dark Matter
• James Webb Space Telescope (JWST)
• Nancy Grace Roman Space Telescope
• SPHEREx (Spectro-Photometer for the History of the Universe and Ices Explorer)
• Stellar Evolution
• The Big Bang
• The Universe

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The expansion of the universe could be a mirage, new theoretical study suggests

New research looking at the cosmological constant problem suggests the expansion of the universe could be an illusion.

The expansion of the universe could be a mirage, a potentially controversial new study suggests. This rethinking of the cosmos also suggests solutions for the puzzles of dark energy and dark matter, which scientists believe account for around 95% of the universe's total energy and matter but remain shrouded in mystery.

The novel new approach is detailed in a paper published June 2 in the journal Classical and Quantum Gravity , by University of Geneva professor of theoretical physics Lucas Lombriser . 

Related: Dark energy could lead to a second (and third, and fourth) Big Bang, new research suggests

Scientists know the universe is expanding because of redshift, the stretching of light's wavelength towards the redder end of the spectrum as the object emitting it moves away from us. Distant galaxies have a higher redshift than those nearer to us, suggesting those galaxies are moving ever further from Earth. 

More recently, scientists have found evidence that the universe's expansion isn't fixed, but is actually accelerating faster and faster. This accelerating expansion is captured by a term known as the cosmological constant , or lambda.

The cosmological constant has been a headache for cosmologists because predictions of its value made by particle physics differ from actual observations by 120 orders of magnitude . The cosmological constant has therefore been described as "the worst prediction in the history of physics." 

Cosmologists often try to resolve the discrepancy between the different values of lambda by proposing new particles or physical forces but Lombriser tackles it by reconceptualizing what's already there..

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"In this work, we put on a new pair of glasses to look at the cosmos and its unsolved puzzles by performing a mathematical transformation of the physical laws that govern it," Lombriser told Live Science via email.

In Lombriser's mathematical interpretation, the universe isn't expanding but is flat and static, as Einstein once believed. The effects we observe that point to expansion are instead explained by the evolution of the masses of particles — such as protons and electrons — over time.

In this picture, these particles arise from a field that permeates space-time. The cosmological constant is set by the field's mass and because this field fluctuates, the masses of the particles it gives birth to also fluctuate. The cosmological constant still varies with time, but in this model that variation is due to changing particle mass over time, not the expansion of the universe. 

In the model, these field fluctuations result in larger redshifts for distant galaxy clusters than traditional cosmological models predict. And so, the cosmological constant remains true to the model's predictions.

"I was surprised that the cosmological constant problem simply seems to disappear in this new perspective on the cosmos," Lombriser said. 

A recipe for the dark universe

Lombriser's new framework also tackles some of cosmology's other pressing problems, including the nature of dark matter. This invisible material outnumbers ordinary matter particles by a ratio of 5 to 1, but remains mysterious because it doesn't interact with light.

Lombriser suggested that fluctuations in the field could also behave like a so-called axion field, with axions being hypothetical particles that are one of the suggested candidates for dark matter. 

These fluctuations could also do away with dark energy, the hypothetical force stretching the fabric of space and thus driving galaxies apart faster and faster. In this model, the effect of dark energy, according to Lombriser, would be explained by particle masses taking a different evolutionary path at later times in the universe.

In this picture "there is, in principle, no need for dark energy," Lombriser added.

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Post-doctoral researcher at the Universidad ECCI, Bogotá, Colombia, Luz Ángela García , was impressed with Lombriser's new interpretation and how many problems it resolves. 

"The paper is pretty interesting, and it provides an unusual outcome for multiple problems in cosmology," García, who was not involved in the research, told Live Science. "The theory provides an outlet for the current tensions in cosmology."

However, García urged caution in assessing the paper's findings, saying it contains elements in its theoretical model that likely can't be tested observationally, at least in the near future.

Editor's note: This article was corrected at 1:30 p.m. ET on June 20, to reflect that redshift is evidence of cosmic expansion, but not evidence of  accelerated cosmic expansion.

Robert Lea is a science journalist in the U.K. who specializes in science, space, physics, astronomy, astrophysics, cosmology, quantum mechanics and technology. Rob's articles have been published in Physics World, New Scientist, Astronomy Magazine, All About Space and ZME Science. He also writes about science communication for Elsevier and the European Journal of Physics. Rob holds a bachelor of science degree in physics and astronomy from the U.K.’s Open University

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• LaraK Is this new? I thought this already was a way to throw out the need for a dark matter and dark energy. Isn't that why protons decaying is something we want to observe? Reply
• Johnnyreddogg Another theoretical and unobserved opinion. Acceleration has already been proven by observation and sound science. Reply
• Aby "In this picture, these particles arise from a field that permeates space-time." How is this different from the Higgs Field? Reply
• Jim H As an amateur observer I have a couple of issues with the assertion that the universe is undergoing an accelerating expansion based on increasing red shift at its distant regions. If the red shift is the same in all directions, does that mean we are at the center of the universe? The raw data that is observed at those great distances is many billions of years old. Reply
• Joe Cogan If the universe is static, then General Relativity, which forbids a static universe, is fundamentally wrong. Given that it's among the most confirmed theories in the history of science, that seems wildly unlikely. And the notion of particle masses fluctuating over time completely blows up Special Relativity, Quantum Mechanics, nuclear physics, cosmology, and chemistry just off the top of my head, so pardon me if I take it less than seriously. Reply

Jim H said: As an amateur observer I have a couple of issues with the assertion that the universe is undergoing an accelerating expansion based on increasing red shift at its distant regions. If the red shift is the same in all directions, does that mean we are at the center of the universe? The raw data that is observed at those great distances is many billions of years old.

Joe Cogan said: If the universe is static, then General Relativity, which forbids a static universe, is fundamentally wrong. Given that it's among the most confirmed theories in the history of science, that seems wildly unlikely. And the notion of particle masses fluctuating over time completely blows up Special Relativity, Quantum Mechanics, nuclear physics, cosmology, and chemistry just off the top of my head, so pardon me if I take it less than seriously.

• Hartmann352 An international team’s project using cosmic microwave background data inferred a Hubble constant of 67, substantially less than the 73 or 74 based on actually measuring the expansion (by analyzing how the light from distant supernova explosions has dimmed over time). When this discrepancy first showed up a few years ago, many experts believed it was just a mirage that would fade with more precise measurement. But it hasn’t. “This starts to get pretty serious,” Adam Riess said at the astronomy meeting. “In both cases these are very mature measurements. This is not the first time around for either of these projects.” One commonly proposed explanation contends that the supernova studies are measuring the local value of the Hubble constant. Perhaps we live in a bubble, with much less matter than average, skewing expansion measurements. In that case, the cosmic microwave background data might provide a better picture of the “global” expansion rate for the whole universe. But supernovas observed by the Hubble telescope extend far enough out to refute that possibility, Riess said. “Even if you thought we lived in a void…, you still are basically stuck with the same problem.” Consequently it seems most likely that something is wrong with the matter-energy recipe for the universe (technically, the cosmological standard model) used in making the expansion rate prediction. Maybe the vacuum energy driving cosmic acceleration is not a cosmological constant after all, but some other sort of field filling space. Such a field could vary in strength over time and throw off the calculations based on a constant vacuum energy. But Riess pointed out that the evidence is growing stronger and stronger that the vacuum energy is just the cosmological constant. “I would say there we have less and less wiggle room.” Another possibility, appealing to many theorists, is the existence of a new particle, perhaps a fourth neutrino or some other relativistic (moving very rapidly) particle zipping around in the early universe. “Relativistic particles — theorists have no trouble inventing new ones, ones that don’t violate anything else,” Riess said. “Many of them are quite giddy about the prospect of some evidence for that. So that would not be a long reach.” Other assumptions built into the current cosmological standard model might also need to be revised. Dark matter, for example, is presumed to be very aloof from other forms of matter and energy. But if it interacted with radiation in the early universe, it could have an effect similar to that of relativistic particles, changing how the energy in the early universe is divided up among its components. Such a change in energy balance would alter how much the universe expands at early times, corrupting the calibrations needed to infer the current expansion rate. It’s not the first time that determining the Hubble constant has provoked controversy. Edwin Hubble himself initially (in the 1930s) vastly overestimated the expansion rate. Using his rate, calculations indicated that the universe was much younger than the Earth, an obvious contradiction. Even by the 1990s, some Hubble constant estimates suggested an age for the universe of under 10 billion years, whereas many stars appeared to be several billion years older than that. Hubble’s original error could be traced to lack of astronomical knowledge. His early overestimates turned out to be signals of a previously unknown distinction between different generations of stars, some younger and some older, Riess pointed out. That threw off distance estimates to some stars that Hubble used to estimate the expansion rate. Similarly, in the 1990s the expansion rate implied too young a universe because dark energy was not then known to exist and therefore was not taken into account when calculating the universe’s age. So the current discrepancy, Riess suggested, might also be a signal of some astronomical unknown, whether a new particle, new interactions of matter and radiation, or a phenomenon even more surprising — something that would really astound a visitor from another universe. See: https://www.sciencenews.org/blog/context/speed-universe-expansion-remains-elusive Recent efforts to measure the Universe further from Earth, like the SH0ES project led by Nobel laureate Adam Riess, have used Cepheids alongside Type Ia supernovae, which was used as a standard candle by Nobel Prize winning Saul Permutter's team when they extrapolated the ever faster expansion rate.. There are also other methods to measure Hubble's constant, such as one that uses the cosmic microwave background - relic light or radiation that began to travel through the Universe shortly after the Big Bang. The problem is that these two measurements, one nearby using supernovae and Cepheids, and one much farther away using the microwave background, differ by nearly 10%. Astronomers call this difference the Hubble tension, and have been looking for new measurement techniques to resolve it. But, the data from a magnified, multiply imaged supernova, which was discovered by a team of astronomers, including Dr Or Graur at the University of Portsmouth, provides insight into a longstanding debate in the field and could help scientists more accurately determine the Universe's age and better understand the cosmos. Hartmann352 Reply
• Kurt Poulsen Yes and no. Expansion is universe in relative. Like time. Every single gravity is universe in relative. Yes black hole is a black hole from outside. From inside is expansion. Not White hole. But universe in relative. Watch that to understand 9cO1O6smTH0 View: https://youtu.be/9cO1O6smTH0 Reply
• Yvonne F What a wonderful article. Nothing in science is ever completely "proven", though many things can be disproven. There is only ever, at best... tons of supporting evidence and no good alternative theories to evaluate and compare. So a whole new way to look at things that causes many inconsistencies with and among current theories is spectacular. Yay for mathematical transformations! Ok maybe that was a little geeky. However if this holds, who knows what else might pop out of the math. Reply
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Teachable Moments | July 24, 2023

Exploring the mystery of our expanding universe.

By Brandon Rodriguez

Learn about a new mission seeking to understand some of the greatest mysteries of our universe, and explore hands-on teaching resources that bring it all down to Earth.

Scientists may soon uncover new insights about some of the most mysterious phenomena in our universe with the help of the newly launched Euclid mission. Built and managed by the European Space Agency, Euclid will use a suite of instruments developed, in part, by NASA's Jet Propulsion Laboratory to explore the curious nature of dark energy and dark matter along with their role in the expansion and acceleration of our universe.

Read on to learn how the Euclid mission will probe these cosmological mysteries. Then, find out how to use demonstrations and models to help learners grasp these big ideas.

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No greater question in our universe promotes wonder in scientists and non-scientists alike than that of the origin of our universe. The Euclid mission will allow scientists to study the nearly imperceptible cosmic components that may hold exciting answers to this question.

Edwin Hubble's observations of the expanding universe in the 1920s marked the beginnings of what's now known as the big-bang theory. We've since made monumental strides in determining when and how the big bang would have taken place by looking at what's known as cosmic background radiation using instruments such as COBE and WMAP in 1989 and 2001, respectively. However, there's one piece of Hubble's discovery that still has scientists stumped: our universe is not only expanding, but as scientists discovered in 1998 , that expansion is also accelerating.

This side by side comparison shows a constant rate of expansion of the universe, represented by the expanding sphere on the left, and an accelerating rate of expansion of the universe, represented by the expanding sphere on the right. Each dot on the spheres represents a galaxy and shows how galaxies move apart from each other faster in the universe that has an accelerating rate of expansion. | Watch on YouTube

This animation shows the changing rate of expansion of the universe due to dark energy. Over the past several billion years, the rate of expansion has changed, yielding a continuous acceleration. On the right, a bubble representing the universe is shown expanding over time – accelerating in its expansion. On the left, a line graph shows the changing expansion speed (y-axis) from 10 billion years ago through now (x-axis). The line starts at 10 billion years ago high on the y-axis and gradually dips downward through about 5.5 billion years ago before turning sharply upward through to the present time. Credit: NASA's Goddard Space Flight Center | › Full video and caption

How can this be? It makes intuitive sense that, regardless of the immense force of the big bang that launched all matter across the known universe 13.8 billion years ago, that matter would eventually come to a rest and possibly even start to collapse. Instead, it's as if we've dropped a glass onto the ground and discovered that the shards are flying away from us faster and faster into perpetuity.

An illustrated timeline of the universe. Credit: WMAP | + Expand image

Scientists believe that answers may lie in two yet-to-be-understood factors of our universe: dark matter and dark energy . Dark matter is unlike the known matter we experience here on Earth, such as what's found on the periodic table. We can't actually see dark matter; we can only infer its presence. It has mass and therefore gravity, making it an attractive force capable of pulling things together. Amazingly, dark matter makes up roughly 27% of the known universe compared with the much more modest 5% of "normal matter" that we experience day to day. However, dark matter is extremely dilute throughout the universe with concentrations of 105 particles per cubic meter.

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This animated pie chart shows rounded values for the three known components of the universe: visible matter (5%), dark matter (27%), and dark energy (68%). Credit: NASA's Goddard Space Flight Center | › Full video and caption

In opposition to the attractive force of dark matter, we have dark energy. Dark energy is a repulsive force and makes up roughly 68% of energy in the known universe. Scientists believe that the existence of dark energy and the amount of repulsion it displays compared with dark matter is what's causing our universe to not only expand, but also to expand faster and faster.

Dr. Jennifer Wiseman, a senior project scientist with the Hubble Space Telescope mission, explains how the mission has been helping scientists learn more about dark energy. Credit: NASA Goddard | Watch on YouTube

But to truly understand this mysterious force and how it interacts with both dark matter and normal matter, scientists will have to map barely detectable distortions of light traversing the universe, carefully measuring how that light changes over time and distance in every direction. As JPL Astrophysicist Jason Rhodes explains, “Dark energy has such a subtle effect that we need to survey billions of galaxies to adequately map it.”

And that's where Euclid comes in.

The European Space Agency and NASA each contributed to the development of the Euclid mission , which launched from Cape Canaveral Space Force Station in Florida on July 1. The spacecraft consists of a 1.2-meter (48-inch) space telescope and two science instruments: an optical camera and a near-infrared camera that also serves as a spectrometer. These instruments will provide a treasure trove of data for scientists of numerous disciplines, ranging from exoplanet hunters to cosmologists.

Light waves get stretched as the universe expands similar to how this ink mark stretches out as the elastic is pulled. Get students modeling and exploring this effect with this standards-aligned math lesson . Credit: NASA/JPL-Caltech | + Expand image

This graphic illustrates how cosmological redshift works and how it offers information about the universe’s evolution. Credit: NASA, ESA, Leah Hustak (STScI) | › Full image and caption

As Gisella de Rosa at the Space Telescope Science Institute explains, “The ancillary science topics we will be able to study with Euclid range from the evolution of the objects we see in the sky today to detecting populations of galaxies and creating catalogs for astronomers. The data will serve the entire space community.”

The cameras aboard Euclid will operate at 530-920 nanometers (optical light) and at 920-2020 nanometers (near infrared) with each boasting more than 576 million and 65 million pixels, respectively. These cameras are capable of measuring the subtle changes to the light collected from celestial objects and can determine the distances to billions of galaxies across a survey of 15,000 square degrees – one-third of the entire sky.

Meanwhile, Euclid's spectrometer will collect even more detailed measurements of the distance to tens of millions of galaxies by looking at redshift. Redshift describes how wavelengths of light change ever so slightly as objects move away from us. It is a critical phenomenon for measuring the speed at which our universe is expanding. Similar to the way sound waves change as a result of the Doppler effect , wavelengths of light are compressed to shorter wavelengths (bluer) as something approaches you and extended to longer wavelengths (redder) as it moves away from you. As determined by a Nobel Prize winning team of astronomers , our universe isn’t just red-shifting over time, distant objects are becoming redder faster.

Euclid will measure these incredibly minuscule changes in wavelength for objects near and far, providing an accurate measurement of how the light has changed as a factor of time and distance and giving us a rate of acceleration of the universe. Furthermore, Euclid will be able to map the relative densities of dark matter and normal matter as they interact with dark energy, creating unevenly distributed pockets of more attractive forces. This will allow scientists to identify minute differences in where the universe is expanding by looking at the way that light is altered or "lensed."

The multi-dimensional maps created by Euclid – which will include depth and time in addition to the height and width of the sky – will inform a complementary mission already in development by NASA, the Nancy Grace Roman Space Telescope . Launching in 2026, this space telescope will look back in time with even greater detail, targeting areas of interest provided by Euclid. The telescope will use instruments with higher sensitivity and spatial resolution to peer deeper into redshifted and faint galaxies, building on the work of Euclid to look farther into the accelerating universe. As Caltech’s Gordon Squires describes it: “We’re trying to understand 90% of our entire universe. Both of these telescopes will provide essential data that will help us start to uncover these colossal mysteries.”

Model the Expanding Universe

Students learn about the role of dark energy and dark matter in the expansion of the universe, then make a model using balloons.

Subject Science

Grades 6-12

Time 30-60 mins

How Do We See Dark Matter?

Students will make observations of two containers and identify differences in content, justify their claims and make comparisons to dark matter observations.

Time Less than 30 mins

Math of the Expanding Universe

Students will learn about the expanding universe and the redshift of lightwaves, then perform their own calculations with a distant supernova.

Grades 9-12

ViewSpace: Dark Energy Videos

Use this collection of short videos to introduce learners to the concept of dark energy.

ViewSpace: Dark Matter Videos

Use this collection of short videos to introduce learners to the concept of dark matter.

Hubble Constant Discrepancies: Implications for Our Expanding Universe

Hear experts discuss how the rate of the universe is measured in different cosmological epochs and what the differences in those measures can tell us.

Roman Space Observer

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• Article for Kids: What Is a Supernova?
• Article for Kids: What Is Dark Matter?
• Article: What Is Dark Energy?
• Article: Gravitational Lensing - Shining a Light on Dark Matter
• Facts & Figures: Euclid Mission - NASA
• Facts & Figures: Nancy Grace Roman Space Telescope

NASA's Universe of Learning materials are based upon work supported by NASA under award number NNX16AC65A to the Space Telescope Science Institute , working in partnership with Caltech/IPAC , Center for Astrophysics | Harvard & Smithsonian , and the Jet Propulsion Laboratory .

TAGS: K-12 Education , Teaching , Teachers , Educators , Resources , Universe , Dark Matter , Dark Energy , Euclid , Nancy Grace Roman Space Telescope , Universe of Learning

Brandon Rodriguez , Educator Professional Development Specialist, NASA-JPL Education Office

Brandon Rodriguez is the educator professional development specialist at NASA’s Jet Propulsion Laboratory. Outside of promoting STEM education, he enjoys reading philosophy, travel and speaking to your dog like it's a person.

Could a 'supervoid' solve an unrelenting debate over the universe's expansion rate?

So-called Hubble Tension could be hinting at new physics.

A major discrepancy between different measurements of our universe's expansion rate could be explained if our galaxy, the Milky Way, sits in a two-billion-light-year-wide void. Such is the conclusion of scientists who argue that a modified theory of gravity can replace the standard model of cosmology. However, this hypothesis is strongly disputed by many astronomers.

The standard model of cosmology describes how we live in a universe dominated by dark energy and dark matter . Dark energy is a mysterious force that is seemingly causing the expansion of the universe to accelerate, while dark matter provides most of the gravity in the universe and is thought to surround galaxies in halo-like shapes while preventing them from sort of falling apart. Together, these elusive phenomena describe how matter is distributed across the cosmos and how galaxies move with respect to one another.

One of the biggest challenges for the standard model of cosmology to overcome, however, is known as the "Hubble Tension." This concept isn't named for the space telescope like you might imagine, but rather its namesake, astronomer Edwin Hubble. In 1929, Edwin Hubble discovered that the more distant a galaxy is, the faster it seems to be moving away from us. He was able to derive a relationship to describe this connection, which subsequently became known as the Hubble–Lemaître Law (after the Belgian theoretical physicist and priest, Georges Lemaître, who independently discovered it too). It says that the velocity with which a galaxy is moving away from us is a product of its distance multiplied by the expansion rate of the universe, which is given by a parameter called the Hubble constant. 

Related: James Webb Space Telescope deepens major debate over universe's expansion rate

Since Edwin Hubble’s day, astronomers have strived to measure the Hubble constant with ever greater accuracy. By knowing the Hubble constant, and therefore precisely how fast the universe is expanding, we can calculate how old the universe must be for it to have reached its present size. Our current best measurements put the universe's age at 13.8 billion years.

However, there is a problem. 

Measurements of the universe's expansion created by measuring the redshifted light of type Ia supernovas have resulted in a Hubble constant value of 73.2 kilometers per second per megaparsec. In other words, it says that every volume of space a megaparsec across (a parsec is 3.26 light years, and a megaparsec is a million parsecs, so 3.26 million light years) is expanding by 73.2 kilometers (45.5 miles) every second.

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Yet, the expansion rate of the universe is also baked into the physics of the cosmic microwave background (CMB) radiation. Measurements of the CMB by the European Space Agency 's Planck mission give a value of the Hubble constant of 67.4 kilometers per second per megaparsec. Both measurements have been made to high accuracy, but they can’t both be correct. 

This strange dichotomy, which has become known as the Hubble Tension, is now arguably the most vexing problem in cosmology. Whereas some astronomers suspect it is the product of a measuring error somewhere along the line, others think it could be hinting at new physics.

That’s exactly what a new paper, from scientists in Germany, Scotland and the Czech Republic, is proposing.

"The universe … appears to be expanding faster in our vicinity — that is, up to a distance of around three billion light years — than in its entirety," says one of the paper's authors, Pavel Kroupa of the University of Bonn in Germany, in a press statement . "And that shouldn’t really be the case."

Their hypothesis centers on an astrophysical oddity called the Keenan–Barger–Cowie supervoid, named after the trio of astronomers who studied it. The supervoid is a so-called "under-density" of matter in the universe, a region where statistically there are fewer galaxies on average — and our Milky Way galaxy just happens to be sitting right in the middle of it, the scientists say. 

Outside of this supervoid, galaxies are packed a little more densely on average, resulting in more gravity that can pull objects within the supervoid towards them. This could give the impression that space is expanding faster in our vicinity, the team suggests, as galaxies are dragged along by the gravity of matter beyond the supervoid.

"That's why they are moving away from us faster than would actually be expected," said co-author Indranil Banik of the University of St Andrews in Scotland.

The standard model of cosmology says that matter should be spread fairly evenly across the universe, and that any voids shouldn't grow beyond a certain size. Therefore, it has some difficulty explaining a supervoid as large as the Keenan–Barger–Cowie void. Some astronomers, including Kroupa and Banik, believe that the standard model cannot explain it, while others such as Martin Sahlén, Iñigo Zubeldía and Joseph Silk of the University of Oxford have gone on record saying that it can.

In Kroupa, Banik and their co-author’s (Sergij Mazurenko of Universität Bonn and Moritz Haslbauer of Charles University in the Czech Republic) hypothesis, our current theory of gravity, and therefore dark matter, is replaced by a new theory called Modified Newtonian Dynamics, or MOND for short. This posits that at low accelerations, gravity behaves differently to how it is described by Einstein and Newton, and that the extra gravity can replace the need for dark matter. In the MOND paradigm, the universe could more easily create large voids like the Keenan–Barger–Cowie supervoid.

However, the idea that the presence of the void can affect measurements of the expansion rate of the universe have been hotly contested in the past. Nobel laureate Adam Riess of Johns Hopkins University in Baltimore, who is leading efforts to measure the Hubble constant with type Ia supernovae, along with W. D'Arcy Kenworthy of Johns Hopkin and Dan Scolnic of Duke University in the United States, showed that type Ia supernovae observed beyond the boundary of the supervoid had the same expansion rate as those inside the void. In response, Kroupa, Banik, Mazurenko and Haslbauer argue that the effect of the supervoid would be felt far beyond the void itself, and so one would expect to measure a higher expansion rate in supernovae beyond the void's confines.

— 'Hubble trouble' could deepen with new measurement of the universe's expansion

—  James Webb Space Telescope could determine if nearby exoplanet is habitable

—  Astronomers may have discovered the closest black holes to Earth

Other methods to measure the Hubble constant, which are independent of the supervoid and the standard model of cosmology, also maintain that the Hubble Tension cannot be explained away. By tracking the angular distance on the sky that water masers in molecular clouds orbiting supermassive black holes in distant galaxies make, and from that deriving their physical distance from geometry, has produced a value of the Hubble constant of 73.9 kilometers per second per megaparsec, which is close to the type Ia supernova measurements, given the uncertainty in the maser measurements. There's also the H0LiCOW (H0 refers to the Hubble constant) project, which studies how light from quasars in the early universe can take different paths of different lengths through foreground gravitational lenses . Quasars often have fluctuations in their brightness; while traversing the different paths through the gravitational lens, the universe is still expanding and the rate of this expansion is imprinted on the different lensed images of the quasar brightness variations. This project finds the expansion rate to be 73.3 kilometers per second per megaparsec, almost identical to the type Ia supernova value. 

These measurements are in conflict with the CMB measurement, and are independent of the hypothesis that the supervoid can create the Hubble tension. So ultimately, if that hypothesis is to have legs, it seems that Kroupa, Banik, Mazurenko and Haslbauer will have to convince a lot more people.

The hypothesis was published in November in the journal Monthly Notices of the Royal Astronomical Society .

For any readers interested in further reading, a list of papers on the subject of the Hubble Tension and their measured values of the Hubble constant can be found here .

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

Keith Cooper is a freelance science journalist and editor in the United Kingdom, and has a degree in physics and astrophysics from the University of Manchester. He's the author of "The Contact Paradox: Challenging Our Assumptions in the Search for Extraterrestrial Intelligence" (Bloomsbury Sigma, 2020) and has written articles on astronomy, space, physics and astrobiology for a multitude of magazines and websites.

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Physical Review D

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Power corrections to the modified QCD perturbative series based on conformal mapping of the Borel plane

Irinel caprini, phys. rev. d 109 , 074002 – published 3 april 2024.

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• INTRODUCTION
• PERTURBATIVE EXPANSIONS OF THE ADLER…
• POWER CORRECTIONS TO THE STANDARD…
• POWER CORRECTIONS TO THE EXPANSION BASED…
• NUMERICAL AND PHENOMENOLOGICAL…
• SUMMARY AND CONCLUSIONS

Modifications of the QCD perturbative expansions by the subtraction of the dominant infrared renormalon have been proposed recently as attempts to solve the longstanding discrepancy between fixed-order and contour-improved perturbation theory for the hadronic τ decays. In this approach, the modified perturbative series is supplemented by a modified gluon condensate in the operator product expansion of the Adler function. Motivated by these works, we revisited recently a formulation of the QCD perturbation theory, proposed some time ago, which takes into account the renormalons by means of the conformal mapping of the Borel plane. One expects that the modified perturbative series obtained in this framework should be accompanied by modified power-suppressed nonperturbative corrections. However, in the previous studies the focus was on the perturbative series and the question of the possible power corrections has not been considered. In the present paper, we investigate for the first time this problem. Using techniques from the mathematical resurgence theory, we derive the expression of the dominant power correction to the perturbative series obtained by conformal mapping of the Borel plane, and discuss its implications for phenomenological applications.

• Received 17 January 2024
• Accepted 15 March 2024

DOI: https://doi.org/10.1103/PhysRevD.109.074002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP 3 .

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The function F ( Q 2 ) defined in ( 4.14 ), truncated at n ≤ 3 , on the Euclidian axis Q 2 > 0 .

Real part (solid line) and imaginary part (dashed line) of the function F ( − s ) , along the circle s = m τ 2 e i ϕ .

Spectral function moments in the framework based on conformal mapping: perturbative series (red points) and power corrections (green points), as functions of the perturbative order n . The multirenormalon Borel model proposed in [ 4 ] was used for generating the higher-order perturbative coefficients.

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High Energy Physics - Theory

Title: the off-shell expansion relation of the yang-mills scalar theory.

Abstract: In this work, we investigate the off-shell expansion relation of the Yang-Mills scalar theory. We have showed explicitly that the single-trace Berends-Giele current in YMS theory can be decomposed into a term expressed by a linear combination of bi-adjoint scalar Berends-Giele currents and one that vanishes under the on-shell limit. We proved that the bi-adjoint scalar currents, as well as the corresponding coefficients, can be characterized by a graphic approach that was originally studied in Einstein-Yang-Mills expansion. Furthermore, we generalized the decomposition to the multi-trace case through unifying relations and established the connection both in single-trace and multi-trace graphic descriptions. Finally, we established the relations between the Yang-Mills currents and the single-trace Yang-Mills scalar currents choosing special reference orders of the Yang-Mills graphs.

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• Published: 04 April 2024

Nickel-catalyzed switchable arylative/ endo -cyclization of 1,6-enynes

• Wenfeng Liu 1   na1 ,
• Wei Li 1   na1 ,
• Weipeng Xu 2 ,
• Minyan Wang   ORCID: orcid.org/0000-0003-3896-5986 2 &
• Wangqing Kong   ORCID: orcid.org/0000-0003-3260-0097 1  

Nature Communications volume  15 , Article number:  2914 ( 2024 ) Cite this article

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• Synthetic chemistry methodology
• Reaction mechanisms

Carbo- and heterocycles are frequently used as crucial scaffolds in natural products, fine chemicals, and biologically and pharmaceutically active compounds. Transition-metal-catalyzed cyclization of 1,6-enynes has emerged as a powerful strategy for constructing functionalized carbo- and heterocycles. Despite significant progress, the regioselectivity of alkyne functionalization is entirely substrate-dependent. And only exo -cyclization/cross-coupling products can be obtained, while endo -selective cyclization/cross-coupling remains elusive and still poses a formidable challenge. In this study, we disclose a nickel-catalyzed switchable arylation/cyclization of 1,6-enynes in which the nature of the ligand dictates the regioselectivity of alkyne arylation, while the electrophilic trapping reagents determine the selectivity of the cyclization mode. Specifically, using a commercially available 1,10-phenanthroline as a ligand facilitates trans -arylation/cyclization to obtain seven-membered ring products, while a 2-naphthyl-substituted bisbox ligand promotes cis -arylation/cyclization to access six-membered ring products. Diastereoselective cyclizations have also been developed for the synthesis of enantioenriched piperidines and azepanes, which are core structural elements of pharmaceuticals and natural products possessing important biological activities. Furthermore, experimental and density functional theory studies reveal that the regioselectivity of the alkyne arylation process is entirely controlled by the steric hindrance of the ligand; the reaction mechanism involves exo -cyclization followed by Dowd-Beckwith-type ring expansion to form endo -cyclization products.

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Directed nickel-catalyzed regio- and diastereoselective arylamination of unactivated alkenes

Leipeng Xie, Shenghao Wang, … Chao Wang

Cationic-palladium catalyzed regio- and stereoselective syn-1,2-dicarbofunctionalization of unsymmetrical internal alkynes

Shubham Dutta, Shashank Shandilya, … Akhila K. Sahoo

Nickel-catalyzed enantioselective reductive carbo-acylation of alkenes

Yun Lan & Chuan Wang

Introduction

The structural diversity of core molecular scaffolds is considered a critical feature of compound libraries, which is decisive for ensuring their success in drug discovery and biological research 1 , 2 , 3 . Compound libraries constructed by traditional synthetic strategies are mainly composed of molecules with similar structures. This is because the structural diversity of the products depends only on the starting scaffolds and building blocks. Therefore, the development of new strategies to efficiently construct structurally distinct and diverse molecular scaffolds, thereby giving rise to compound libraries with differing and selective biological activities is of great siginificance 4 , 5 . Ligand-directed divergent synthesis (LDS) is highly sought-after in library synthesis because it allows the construction of structurally diverse molecular scaffolds from common starting materials by simply changing the ligands of metal catalysts 6 . However, it is undoubtedly the most challenging strategy because ligand design alone requires subversion of the inherent regiopreferences of reactants and metal centers.

Cyclic scaffolds, especially heterocycles, are ubiquitous in natural products, pharmaceuticals, and numerous functional molecules. The development of effective methods for the rapid construction of various cyclic compounds represents one of the major domains of synthetic organic chemistry. In this regard, transition-metal-catalyzed cycloisomerization 7 , 8 , 9 , 10 , 11 and reductive cyclization 12 , 13 , 14 , 15 , 16 of 1,6-enynes have been established to generate five-membered (hetero)cycles. Advances along this line have revealed some intriguing transition metal-catalyzed functionalizing cyclization reactions, providing efficient and convenient access to a wide array of elusive cyclic systems 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 . The appeal of these cyclizations lies in the streamlining construction of structurally complex and functionalized cyclic scaffolds from readily accessible 1,6-enynes. From a reaction mechanism perspective, these transformations are primarily initiated by the formation of metalacyclic intermediates via oxidative cyclization pathways or the formation of alkenyl metal species via carbometallation processes. The former has been well explored 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , but controlling the regioselectivity of the latter is difficult, usually in two ways: α-insertion or β-insertion (Fig.  1a ) 35 , 36 , 37 , 38 . 5- Exo -cyclization of the resulting alkenyl-metal intermediate I (via β-insertion) would provide the conventional five-membered ring product III bearing an exocyclic double bond. Alternatively, α-insertion followed by E/Z isomerization 39 , 40 , 41 , 42 , 43 , 44 would afford alkenyl-metal intermediate II , which undergoes 6- exo cyclization to afford six-membered ring product V possessing an endocyclic double bond. Despite enormous efforts, these strategies still suffer from many limitations: the regioselectivity of alkynes insertion into organometallic species is entirely substrate-dependent (electronic or steric effects of substituents on alkynes). Furthermore, since exo -cyclizations are anyway kinetically superior to the corresponding endo -cyclizations, 6- endo- or 7- endo- cyclization products are rarely obtained 45 , 46 , 47 , 48 .

a The state of the art of transition metal-catalyzed arylative cyclization of 1,6-enynes; b Ligand-controlled regiodivergent arylative cyclization of 1,6-enynes.

Nickel-catalyzed reductive cross-coupling has been emerged as a powerful and straightforward method for constructing carbon-carbon bonds 49 , 50 , 51 , 52 , 53 , 54 . Furthermore, due to its unique properties, nickel has been used in a range of ligand-controlled divergent transformations 55 , 56 , 57 . To address the major remaining challenges of 1,6-enyne cyclization, we were curious whether changing the structure and/or electronegativity of the ligands in nickel catalysts would enable regioselective and switchable arylation of alkynes. Here, we demonstrate that judicious choice of ligands enables the switchable arylation/ cyclization of 1,6-enynes, in which the nature of the ligand dictates the regioselectivity of alkyne arylation, while the electrophilic trapping reagents determine the selectivity of the cyclization mode. Specifically, in the presence of electron-deficient alkenes, using a commercially available 1,10-phenanthroline as a ligand facilitates trans -arylation/ endo- cyclization to obtain seven-membered ring products, while a 2-naphthyl-substituted Bisbox ligand promotes cis -arylation/ endo- cyclization to access six-membered ring products (Fig.  1b ). Diastereoselective cyclizations have also been developed for the synthesis of enantioenriched piperidines and azepanes, which are core structural elements of pharmaceuticals and natural products possessing important biological activities. This transformation is modular, with the ligand rather than the substrate precisely determining the regioselectivity of alkyne arylation process, and the electrophilic trapping reagents determining the regioselectivity of cyclization. Such ligand-directed divergent synthesis (LDS) remains hitherto elusive despite persistent interest.

Results and discussion

Reaction development.

To test our hypothesis, we started our investigation by evaluating the nickel-catalyzed three-component cascade cyclization of 1,6-enyne ( 1 ) with PhBr ( 2 ) and trifluoromethyl alkene ( 3 ) (Table  1 ). After a series of experiments, a combination of NiBr 2 (DME), 1,10-phenanthroline L4 , Mn, CsF, and DMA at 60 °C afforded gem -difluoroallylated seven-membered ring product 4 in 63% isolated yield with exquisite regioselectivity ( 4 / 5  = 20/1) (entry 1). Inferior results were observed when either TBAI or NaI was used instead of CsF (entries 2 and 3). Lowering the reaction temperature to 40 °C resulted in no reaction, while increasing the reaction temperature to 80 °C resulted in lower yield (entries 4 and 5). Traces, if any, of 4 were observed when Zn was used instead of Mn as the terminal reducing agent (entry 6). Notably, the direct reductive coupling of aryl bromides and trifluoromethyl alkenes in this catalytic system is well suppressed.

We evaluated a range of different ligands with the goal of identifying the conditions for switchable access to the seven-membered ring product 4 and the six-membered ring product 5 . 2,2′-Bipyridine ( L1-L3 ) and 1,10-phenanthroline ( L4 ) favored the formation of 4 , especially the latter providing 4 in higher yield and excellent regioselectivity (entries 7–10). Strikingly, under the same reaction conditions as shown in entry 10, the use of relatively electron-rich Pyrox L5 or Bisbox L6 as ligands resulted in a regioselective switch en route to 5 , albeit in lower yields (entries 11 and 12). We further synthesized a series of Bisbox ligands with different substituents on the oxazoline ring and examined their performances. The phenyl-substituted ligand L7 showed slightly higher regioselectivity ( 4 / 5  = 1/8, entry 13). The benzyl-substituted ligand L8 provided 5 in 58% yield and improved the regioselectivity to 1:15 (entry 14). Using a 2-naphthyl-substituted Bisbox ligand L9, 5 was obtained in 71% isolated yield and excellent regioselectivity ( 4 / 5  = 1:28) (entry 15). These results clearly demonstrate that the backbone of the ligand determines the regioselectivity pattern.

Having identified optimal reaction conditions for the ligand-controlled divergent synthesis of seven- and six-membered ring products, we turned our attention to investigating the scope and limitations of those two protocols. We first explored the trans- arylative/ endo cyclization protocol for the selective synthesis of seven-membered ring products using ligand L4 (Fig.  2 ). In terms of 1,6-enynes, the carbon-tethered and nitrogen-tethered 1,6-enynes were examined, and the corresponding products 6 and 7 were obtained as expected. The molecular structure of 7 was unambiguously confirmed by single-crystal X-ray diffraction analysis. Electron-donating (OMe) or electron-withdrawing groups (CF 3 , CN) on the aromatic ring at the alkyne terminal (R 1 ) were found to be compatible, leading to the corresponding products 8 - 10 in 49-69% yields. Notably, chlorine substitution on the aromatic ring also proceeded smoothly, affording 11 in 68% yield, providing an opportunity for further derivatization of the obtained product. Complex molecules such as estrone could also be successfully incorporated into product ( 12 ). Nonetheless, alkyl-substituted alkynes and terminal alkynes failed to produce the expected products. Introduction of a phenyl group on the alkene moiety did not preclude the transformation ( 13 ).

a Scope of 1,6-enynes; b Scope of aryl halides; c Scope of electron-deficient alkenes.

We then evaluated the scope of aryl (pseudo)halides. We were pleased to find that the presence of electron-donating and electron-withdrawing groups at the para or meta position of the aromatic ring did not affect selectivity and efficiency ( 14 – 23 ). Aryl triflate was also tolerated as shown by the efficient formation of product 15 . Heteroaryl bromides such as 5-bromo-2-methoxypyridine, 3-bromothiophene, 2-bromodibenzofuran, 2-bromodibenzothiophene, 5-bromobenzofuran, 5-bromoindole, and 3-bromocarbazole were all efficiently transformed into the corresponding products ( 24 – 30 ) in satisfactory yields.

The generality of the electron-deficient alkenes was also investigated. Trifluoromethyl alkenes with various useful functional groups, such as cyano, ester, amide, sulfonate, trifluoromethoxy, chloro, and alkoxy on the aromatic ring, could be successfully transferred to the corresponding products ( 31 – 40 ). In addition, quinoline, benzothiophene and carbazole-substituted trifluoromethyl alkenes ( 41, 42 and 43 ) were also compatible with the reaction conditions. The seven-membered ring product 44 and 45 were also obtained under the same reaction conditions when electron-deficient alkenes such as acrylate or vinyl sulfone were used respectively.

We next examined the scope of the cis- arylative/ endo cyclization protocol for the selective synthesis of six-membered ring products using ligand L9 (Fig.  3 ). Similar to what we observed with the trans- arylative/ endo cyclization, C- or N-tethered 1,6-enynes had little effect on the reactivity and selectivity, providing the corresponding products ( 46 - 47 ) in 58–63% yields. 1,6-Enynes with substituents on the alkene moiety such as phenyl and ester were also compatible ( 48 - 49 ). Both electron-withdrawing (Cl) and electron-donating groups (OMe) on the aromatic ring at the alkyne terminal (R 1 ) were found to be compatible ( 50 - 51 ).

a Scope of 1,6-enynes; b Scope of aryl halides; c Scope of electron-deficient alkenes. a The ratio of product to reduced Heck product was determined by 19 F NMR spectroscopy.

Aryl (pseudo)halides with versatile functional groups were then examined. It is noteworthy to mention that substrates with both electron-donating and withdrawing groups proceed smoothly to afford the corresponding products ( 52 - 58 ) in moderate to good yields. In particular, the p -chlorine substituted product 54 and the 3-bromocarbazole substituted product 59 were both isolated in good yields.

In addition, the compatibility of the transformation with various trifluoromethyl alkenes was evaluated in a robustness screening. A series of valuable functional groups such as cyano, ester, amide, sulfonate, ketone, trifluoromethoxy, chloro, and alkoxy were all well-tolerated ( 60 – 69 ). Trifluoromethyl alkenes bearing heterocyclic groups could also be transformed into the desired products 70 – 73 in moderate yields. In the case of the trifluoromethylalkenes with a strong electron-donating group, the desired defluorinative products 68 – 72 were isolated in a mixture with the reductive Heck coupling products which retained the trifluoromethyl group.

Enantiomerically pure N -heterocyclic compounds, especially piperidines and azepanes, represent important motifs in pharmaceutically important natural alkaloids 58 . Consequently, it is of great significant to develop reliable synthetic methods for the synthesis of such heterocycles. We screened a series of chiral ligands in an attempt to render the reaction asymmetric (Supplementary Table  1 ). Simultaneously controlling the regioselectivity of alkyne migratory insertion and the stereoselectivity of the cyclization process is indeed a very challenging task, and all our attempts resulted in only racemic products.

We turned to developing a solution to obtain enantioenriched piperidines and azepanes by diastereoselective cyclization of substrates with pre-existing stereocenters 59 , 60 . Enantioenriched 1,6-enyne 74 (e.r. > 99:1) was prepared employing Ellman’s auxiliary 61 to test subsequent ligand-controlled arylative cyclization for the divergent synthesis of chiral piperidines and azepanes (Fig.  4a ). Excitingly, by a simple ligand switch, enantioenriched piperidines 75–82 and azepanes 83–86 can be obtained, respectively, from the same starting materials in synthetically useful yields and excellent diastereoselectivities (15:1 to > 20:1 d.r.). The absolute configuration of 76 was determined by single-crystal X-ray diffraction analysis, and that of all other products were assigned accordingly.

a Diastereoselective synthesis of enantioenriched piperidines and azepanes; b Diarylative cyclization of 1,6-enynes.

We further found that the reaction of 1,6-enyne with aryl bromide underwent trans -arylative exo -cyclization/cross-coupling to give diarylated products when 1,10-phenanthroline L4 was used as a ligand (Fig.  4b ). The presence of electron-donating and electron-withdrawing groups at the para - or meta -position of the aryl bromides does not affect selectivity and efficiency ( 87 – 95 ). Diastereoselective diarylative cyclization gave enantioenriched piperidine 96 in excellent diastereoselectivity ( > 20:1 d.r.). Despite extensive attempts, cis -arylation cyclization/cross-coupling products have not yet been obtained using L9 as a ligand.

Mechanistic investigation

To shed light on the reaction mechanism, we designed a series of experiments as outlined in Fig.  5 . First, Ph-Ni(II)Br complex 98 and 99 were synthesized and submitted to the reactions with 1,6-enyne 97 and trifluoromethyl alkene 3 under our standard reaction conditions. The corresponding products 7 and 47 were obtained in 31% and 30% yields, respectively (Fig.  5a ). These results clearly demonstrate that active aryl-nickel(II) species are generated during the reaction and that the ligand determines the regioselectivity alkyne arylation.

a Reactions with arylnickel complex; b Reaction of trifluoromethyl alkene with alkenyl iodide; c Deuterium experiments; d Proposed reaction pathways; e Reaction of deuterated 1,6-enyne, aryl bromide and trifluoromethyl alkene.

We further synthesized alkenyl iodide 100 and subjected to the reaction with trifluoromethylalkene 3 under standard conditions. The target product 7 was isolated in 65% yield, evidently confirming the formation of the key alkenyl-nickel intermediate and the involvement of cis / trans isomerization of alkenyl-nickel species during the reaction (Fig.  5b ). Deuterium labeling experiments were performed. Reaction of 100 with 5 equivalents of D 2 O afforded the deuterated exo -cyclization product 101-D in 43% yield. Reaction of 100 with trifluoromethylalkene 3 in the presence of 10 equivalents of D 2 O gave product 101-D and 7 in 24% and 49% yield, respectively (Fig.  5c ). These deuterated products should result from deuteration of the corresponding organonickel intermediates, suggesting that both 6- exo -cyclization and 7- endo -cyclization of alkenyl-nickel intermediate appear to be possible.

Three possible reaction pathways are proposed to explain the transformation of six-membered-ring nickel intermediate 103 to seven-membered-ring nickel intermediate 106 in Fig.  5d . Considering that β-carbon elimination from a non-strained metal complex is a high energy process 62 , 63 , 64 , a retro 6- exo cyclization via β-carbon elimination followed by 7- endo cyclization deemed less probable (Path I, Fig.  5d ).

To verify 1,2-dyotropic rearrangement mechanism (Path II, Fig.  5d ), deuterated 1,6-enyne ( Z )- 107 - D was prepared and subjected to the reaction with trifluoromethylalkene 3 and PhBr under standard conditions. Product 7-D was isolated in 55% yield with 1:1 diastereoselectivity (Fig.  5e ). Although this process is non-stereoselective, considering the carbon-nickel bond is easily undergo homolytic cleavage to generate the corresponding carbon radical and then recombine, we cannot rule out the mechanism of 1,2-dyotropic rearrangement 65 , 66 , 67 .

Furthermore, Dowd-Beckwith ring expansion process was also considered (Path III, Fig.  5d ) 68 , 69 , that is, the primary radical intermediate 104 and the tertiary radical intermediate 105 coexist in the reaction system; the type of electrophilic trapping reagents determine the structure of products. When cross-coupling with aryl bromides via an oxidative addition/reductive elimination mechanism, primary radicals 104 are preferred because the process is more sensitive to steric hindrance of ligands. The nucleophilic tertiary radicals 105 are favored when cross-coupling with less hindered electron-deficient alkenes (acrylates or trifluoromethyl alkenes) via Giese addition.

DFT calculations

To better understand the reaction mechanism and the origin of selectivity-controlled steps of arylative of alkynes with different ligands, density functional theory (DFT) studies were performed (Fig.  6 ) 70 . The computed energy profile for the nickel catalytic cycle using ligand L4 is shown in Scheme 8 A, while the influence of ligand L9 is shown in Supplementary Fig.  6 . The overall pathway commences with the coordination of bromobenzene 2 to the in-situ generated Ni(0)/ligand species, forming intermediate INT1A . The oxidative addition of the C−Br bond proceeds through transition TS2A and subsequent substrate 1 replaces the Br − ligand at INT2A , resulting in the formation of INT3A . The noncovalent interactions (NCI) between substrates and ligands is more pronounced for the regioselectivity of migratory insertion (Fig.  6b ) 71 , 72 . In the case of smaller ligand L4 , phenyl connected with nickel center and phenyl substituent of alkyne are the most sterically congesting moiety, thus resulting the energy barrier of transition state TS4A-L4 is 4.9 kcal mol −1 higher than that of transition state TS4B-L4 (17.8 vs 12.9 kcal mol −1 ). The α-migratory insertion to form intermediate INT4B-L4 is kinetically more favorable pathway. For ligand L9 , there is a significant attractive interaction between naphthyl group and phenyl unit of alkyne, rendering an increased energy barrier of TS4B-L9 to 21.8 kcal mol −1 . This result illustrates intermediate INT3A-L9 favors β-insertion over α-insertion. The resulting intermediate INT4B-L4 undergoes rapid cis/trans isomerization via reversible Ni–C bond homolysis 73 , 74 , 75 or a η 2 -coordinated alkenylnickel species (see Supplementary Information for details) 76 , 77 , 78 to form intermediate INT5B-L4 , which facilitates the proximity of the nickel(II) center to the C = C bond for the subsequent cyclization process 35 , 79 , 80 . The competitive cyclization modes with ligand L4 and L9 are further investigated, respectively (Fig.  6c ). Compared to the endo -cyclization, the exo -cyclization through TS5B-L4-exo and TS5A-L9-exo is a more favorable process (14.3 vs 11.3 kcal mol −1 for L4 and 19.4 vs 2.8 kcal mol −1 for L9 ). Upon adding D 2 O, the generated INT5B-L4-exo can be converted into six-membered skeleton smoothly, consistent with the experimental observation shown in Fig.  6c . Finally, the Ni(II)-alkyl bond of intermediate INT5B-L4-exo and INT5A-L9-exo undergoes homolytic cleavage to generate alkyl radical and Ni(I) species, which was then reduced by the present of Mn to regenerate INT1A , completing nickel catalytic cycle.

a The calculated energy profile of the nickel-catalyzed cycle using ligand L4 ; b The competitive migratory insertion of aryl-nickel into alkyne with ligand L4 and L9 ; c The competitive cyclization modes with ligand L4 and L9 .

Furthermore, extensive computational studies on alkyl-nickel(II) species INT5B-L4-exo and INT5A-L9-exo were performed (Fig.  7a, b ). We located a homolytic cleavage pathway of alkyl-nickel(II) to generate radical INT7B (Fig.  7a ). By comparison, the alternative pathways involving directly insertion into the double bond of trifluoromethyl alkene 3 ( TS6A-L4-exo and TS6A-L9-exo, ∆G ≠   = 24.0 and 33.0 kcal mol −1 , respectively), 1,2-alkenyl/Ni concerted dyotropic rearrangement ( TS6C-L4-exo and TS6C-L9-exo, ∆G ≠   = 41.5 and 47.2 kcal mol −1 , respectively), and 1,2-alkyl/Ni concerted dyotropic rearrangement ( TS6D-L4-exo and TS6D-L9-exo, ∆G ≠   = 52.1 and 57.7 kcal mol −1 , respectively), were calculated to be kinetically unfavorable.

a Extensive computational studies on alkyl-nickel(II) species INT5B-L4-exo ; b Extensive computational studies on alkyl-nickel(II) species INT5A-L9-exo .

The subsequent pathway for the generated radical INT7B was shown in Fig.  8 . The radical induced Dowd-Beckwith-type ring expansion 68 , 81 , 82 , 83 , 84 , 85 through transition TS8B and TS9B , leading to the formation of seven membered ring radical INT9B . After that, INT9B captured by substrate 3 leads to the formation of INT10B with an activation free energy barrier of 7.9 kcal mol −1 . For the enantiomerically pure N -heterocyclic compound 72 , the radical addition preferentially occurred at the less steric hindrance to result excellent diastereoselectivities. Owing to the computed high energy barrier ( TS11B, ∆G ≠   = 29.6 kcal mol −1 ), the direct β-F elimination of INT10B is excluded. The single electron transfer (SET) process between INT10B and reductant Mn proceeds to afford anion INT11B , which is followed by β-F elimination via transition state TS12B with an activation energy of 9.9 kcal mol −1 , yielding the desired product 4 . The energy profile for the radical produced by INT5A-exo-L9 is also calculated to obtain product 5 (for the details of the computational data, see Supplementary Fig.  8 ). The frontier molecular orbital theory is further used to analysis the reactivity of the generated radicals (Fig.  8c ). Compared with radical INT7B , the radical INT9B with higher SOMO energy exhibits more nucleophilicity, which should be thermodynamically more favorable to attack electron-deficient alkenes to generate radical INT10B , delivering the desired cyclization products.

a The calculated energy profile from radical INT7B to product 3 ; b The structure of various transition states; c The frontier molecular orbital theory is further used to analysis the reactivity of the generated radicals.

Proposed reaction mechanism

Based on the above experimental and DFT studies, a plausible catalytic cycle is outlined in Fig.  9 . Oxidative addition of aryl bromide to Ni(0) species produces aryl-nickel(II) species. The steric interaction between the ligands and substrates precisely controls the regioselectivity of the migratory insertion of aryl-nickel(II) species into alkynes, where L9 promotes β-insertion to form alkenyl-nickel(II) intermediate A and L4 facilitates α-insertion to form alkenyl-nickel(II) intermediate E . Intermediates A and E undergo highly selective exo -cyclization to give alkyl-nickel(II) intermediates B and F , which then undergo homolytic cleavage to afford the corresponding primary alkyl radical intermediates C and G , respectively. Direct cross-coupling of radical G with aryl bromides in the presence of Ni(0) gives diarylated products. Intermediates C and G undergo Dowd-Beckwith ring expansion to form more stable tertiary radical intermediates D and H , respectively. Finally, radical addition followed by fluorine elimination will furnish the corresponding six- and seven-membered ring products, respectively.

Rationally explain the ligand-controlled regiodivergent arylation of alkynes and cyclization processes.

The structure of the final products is related to the nature of the electrophilic trapping reagents. The primary radical G may react preferentially because it is formed first and is more kinetically accessible. The tertiary radicals D and H , although more crowded, are more stable and survive longer in the reaction system. When reacting with ArBr via an oxidative addition/reductive elimination mechanism, primary radicals C and G are preferred because the process is more sensitive to steric hindrance of the ligand. More nucleophilic tertiary radicals D and H are favored when reacting with electron-deficient alkenes such as trifluoromethylalkenes or acrylates via Giese addition.

General procedure for the synthesis of 7-membered ring products

An oven-dried sealed tube equipped with a PTFE-coated stir bar was charged with NiBr 2 (DME) (10 mol%), L4 (20 mol%), trifluoromethyl alkene (0.1 mmol), 1,6-enyne (0.2 mmol), CsF (1.0 equiv), Mn powder (3.0 equiv), aryl bromide (2.0 equiv) and anhydrous DMA (2 mL). The sealed tube was sealed and removed from the glovebox. Then the reaction was stirred at 60 o C until the reaction was complete (monitored by TLC). The resulting mixture was quenched with saturated NH 4 Cl solution (5 mL) and further diluted with water (10 mL). The aqueous layer was extracted with EtOAc and the combined organic layers were washed with brine, dried over anhydrous Na 2 SO 4 , filtered, and concentrated under vacuum. The residue was purified by chromatography on silica gel, eluting with PE/EtOAc (50/1 ~ 5/1) to afford the desired 7-membered ring products.

General procedure for the synthesis of 6-membered ring products

An oven-dried sealed tube equipped with a PTFE-coated stir bar was charged with NiBr 2 (DME) (10 mol%), L9 (20 mol%), trifluoromethyl alkene (0.1 mmol), 1,6-enyne (0.2 mmol), Mn powder (3.0 equiv), aryl bromide (2.0 equiv) and anhydrous DMA (2 mL). The sealed tube was sealed and removed from the glovebox. Then the reaction was stirred at 60 o C until the reaction was complete (monitored by TLC). The resulting mixture was quenched with saturated NH 4 Cl solution (5 mL) and further diluted with water (10 mL). The aqueous layer was extracted with EtOAc and the combined organic layers were washed with brine, dried over anhydrous Na 2 SO 4 , filtered, and concentrated under vacuum. The residue was purified by chromatography on silica gel, eluting with PE/EtOAc (50/1 ~ 5/1) to afford the desired 6-membered ring products.

Data availability

The authors declare that all the data supporting the findings of this work are available within the article and its Supplementary Information files or from the corresponding author upon request. The X-ray crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers 2220556 ( 7 ), 2220555 ( 46 ), and 2240774 ( 74 ). CIF files and crystal structure data are available in the Supplementary Information and Supplementary Data  1 .

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Acknowledgements

Financial support provided by the National Natural Science Foundation of China (22171215 and 22171134), the Hubei Provincial Outstanding Youth Fund (2022CFA092), the National Key R&D Program of China (2022YFA1503200), and GuangDong Basic and Applied Basic Research Foundation (2022A1515010246). The authors also thank the High-Performance Computing Center of Nanjing University for doing the numerical calculations in this paper on its blade cluster system.

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The Institute for Advanced Studies (IAS), Wuhan University, Wuhan, 430072, China

Wenfeng Liu, Wei Li & Wangqing Kong

State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210023, China

Weipeng Xu & Minyan Wang

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W.K. and WF.L. conceived and designed the project. WF.L. and W.L. conducted the experiments. W.K., WF.L. and W.L. analyzed and interpreted the experimental data. M.W. and W.X. performed the DFT calculations. W.K. and M.W. prepared the manuscript. WF.L. and W.L. prepared the Supplementary Information. All authors contributed to discussions.

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Liu, W., Li, W., Xu, W. et al. Nickel-catalyzed switchable arylative/ endo -cyclization of 1,6-enynes. Nat Commun 15 , 2914 (2024). https://doi.org/10.1038/s41467-024-47200-z

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DOI : https://doi.org/10.1038/s41467-024-47200-z

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