What is the acceleration for the expansion of the Universe?

What is the acceleration for the expansion of the Universe?

I've found that the speed of expansion is about $70frac{km}{scdot 10^{6}pc}$.

But what is the acceleration of expansion in terms of $frac{km}{s^{2}cdot 10^{6}pc}$ ?

I want to know how fast this value of "70" is changing, ie what is $mathrm{d}H_0/mathrm{d}t$?

The figure below shows the evolution of the Hubble parameter $H$ from 10 billion years (Gyr) ago, to 10 Gyr into the future:

As you can see, the change in $H$ is modest nowadays, compared to the past. The "acceleration" of the expansion at any point in time is given by the tangent to the curve at that time. Today, the change is $dH/dt simeq -1.2,mathrm{km},mathrm{s}^{-1},mathrm{Mpc}^{-1},mathrm{Gyr}^{-1}$, or roughly $-10^{-17},mathrm{km},mathrm{s}^{-2},mathrm{Mpc}^{-1}$.

In other words, it will take roughly a billion years before the expansion rate has decreased by $1,mathrm{km},mathrm{s}^{-1}$, and it asymptotically approaches some $57,mathrm{km},mathrm{s}^{-1}$.

Since $H$ is defined as $(da/dt),/,a$, where $a$ is the scale factor (the "size" of the Universe), a constant $H$ implies that $apropto e^{Ht}$; that is, the size of the Universe increases exponentially.

You have 1pc=3.26ly=3.26*300000*365.25*24*3600 km =…

So you could easily find H0 :)


Sorry I've read to quickly the question. The acceleration rate of the universe is given by second equation of Friedmann Lemaître.

$$frac{ddot{a}}{a} = -frac{4 pi G}{3}left( ho+frac{3p}{c^2} ight) + frac{Lambda c^2}{3}$$

with $ ho$ and p density of the fluids (matter, dark energy… ) you consider in the cosmological (standard) model.

The acceleration of the universe is written as $dot{H}$, where $H$ is the Hubble Rate (today, the Hubble Rate is given the name the Hubble Constant, $H_0$, and is given the value of 70 km/s/106pc). The Friedmann Equation can be simplified to the form:

$$dot{H} + H^2 = -frac{4pi G}{3}left( ho + frac{3p}{c^2} ight)$$

Where $ ho$ is the density, and $p$ is the pressure. $G$ is the gravitational constant, and $c^2$ is the speed of light.

Now, to find the acceleration, simply substitute the relavent values into the equation below:

$$dot{H_0} = -frac{4pi G}{3}left( ho_0 + frac{3p_0}{c^2} ight) - H^2_0$$

I will try to find the relavent values, but as the previous answer says, the value is roughly $-10^{-17},mathrm{km},mathrm{s}^{-2},mathrm{Mpc}^{-1}$

Pela's answer gives the numerical value, I thought I would just explain the difference between $dot{H}$, which is negative, and an acceleration, which is positive.

The Friedmann acceleration equation is given by $$frac{ddot{a}}{a} = -frac{4 pi G}{3}left( ho+frac{3p}{c^2} ight) + frac{Lambda c^2}{3}, ag*{(1)}$$ whilst the Hubble parameter is defined as $$H = frac{dot{a}}{a} ag*{(2)}$$

In equation (1) the first term gets smaller with time since both matter density $ ho$ and pressure $p$ due to matter and radiation become smaller. The second term due to the cosmological constant $Lambda$ is positive and eventually dominates and we are in that regime now. This is what is meant by an accelerating universe, where the second derivative of the scale factor $ddot{a}$ is positive.

However, you have modified your question to ask what the time derivative of the Hubble parameter (not constant!) is. Differentiating equation (2) with respect to time, we have $$dot{H} = frac{ddot{a}}{a} - H^2$$ $$dot{H} = -frac{4 pi G}{3}left( ho+frac{3p}{c^2} ight) + frac{Lambda c^2}{3} - H^2 ag*{(3)}, .$$

$dot{H}$ is the gradient of the plot shown in Pela's answer and it is negative. That is $H$ is getting smaller. As the universe gets bigger, $H$ reaches its asymptotic value when $ddot{a}/a = H^2$.

Nobel Prize 'Inevitable' for Accelerating Universe Discovery, Physicists Say

For the three astrophysicists who won the Nobel Prize in physics today (Oct. 4), it was only a matter of when, not if, they would get the prize, their peers said. Their discovery that the universe's expansion is accelerating was an Earth-shattering revelation that led to the bizarre concept of dark energy.

For such a monumental find, experts said, the Nobel was inevitable.

"We expected it from the day the research paper was published back in the1990s,"astrophysicist Neil deGrasse Tyson, director of the Hayden Planetarium at the American Museum of Natural History, told "The fact that there's a committee in Sweden who agrees with what we've known all along is not a surprise to us in the astrophysics community. It is a discovery that's bigger than the prize itself."

The Nobel Prize committee announced the decision today to award 2011's prize to Saul Perlmutter of the Lawrence Berkeley National Laboratory and the University of California, Berkeley Brian Schmidt of the Australian National University and Adam Riess of Johns Hopkins University and the Space Telescope Science Institute.

Perlmutter headed up one team, and Schmidt and Riess another. They independently found that the ballooning of the universe over time is speeding up, contrary to all expectations. [7 Surprising Things About the Universe]

Scientists were left scratching their heads regarding the cause of this speeding up of the universe's expansion, which wouldn't be possible unless there was a force working against the inward pull of gravity. This force they have named "dark energy."

"All we can say is that there's an entity that is forcing the universe to accelerate outside of the wishes of gravity," Tyson said. "The term 'dark energy' seems apt, but we don&rsquot know what it is &mdash that remains a mystery. The Nobel is for the discovery of this mystery."

The researchers, in fact, had set out to find the opposite: to measure just how much the expansion of the universe was decelerating, as it was expected to do because of gravity.

"They wanted to know to what extent gravity is slowing down the expansion of the universe &mdash and their rivalry to 'get there first' was fierce," said journalist Richard Panek, who wrote a book about the discovery called "The 4% Universe: Dark Matter, Dark Energy, and the Race to Discover the Rest of Reality" (Houghton Mifflin Harcourt, 2011). "What they discovered instead is that the universe is doing the opposite of what they expected &mdash that the expansion is speeding up under the influence of some force that, on the cosmic scale, is overpowering gravity. Scientists want to catch the universe doing something weird, and they caught it doing the weirdest thing of all."

The mind-bending measurement, made by studying faraway star explosions called Type 1a supernovas that allowed the researchers to precisely measure cosmic distances, shook all of science.

"It was revolutionary for physics and cosmology," said John Carlstrom,director of the Kavli Institute for Cosmological Physics at the University of Chicago."The acceleration and that there is some sort of dark energy is now widely accepted by experts in the field. Now if only we could understand what the dark energy really is! That is one of the biggest mysteries in all of physics."

Other experts agreed that the dark energy revealed by Perlmutter, Schmidt and Riess will play a defining role in scientists' quest to understand the universe going forward. [What is Dark Energy?]

"Arguably understanding the nature of dark energy is the biggest challenge that physics is facing today," said Mario Livio, a colleague of Riess' at the Space Telescope Science Institute. "While dark energy has not played a huge role in the evolution of the universe in the past, it will play the dominant role in the evolution in the future. The fate of the universe depends on the nature of dark energy. I am clearly very excited about Adam, Saul, and Brian winning the prize."

And the significance of the discovery extends even beyond the fate of our universe, to the question of whether there are in fact multiple universes, with different amounts of dark energy in each.

"The discovery was amazing," said Harvard University theoretical physicist Lisa Randall, author of the new book "Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World" (Ecco, 2011). "For many, it changed their research agenda. I speak especially of those who work on the 'landscape' of multiple universes and the 'anthropic principle' that says we can live only in a universe with such small dark energy."

In 1998 it was announced that the expansion of the universe is accelerating. What does this imply from the perspective of the big bang?

After studying type 1a supernova far away astronomers have found that the universe is not only expanding but accelerating.


Type 1a supernovas are standard candles and can be used for calculating distances where Cepheid can not b e used..THe reason for a acceleration is dark energy an unknown force..This reduces the chances for a big crunch.
picrture credit

The implications of an expanding universe that is accelerating is that the universe will not reverse and never stop its expansion, so the universe will have an ending and had a beginning.


Before 1998 many people believed that the universe was eternally expanding and contracting. The so called rubber ball theory popularized by Asimov allowed the belief in an eternal self existent universe. That the universe is expanding at an accelerating rate rules out the rubber ball theory.

If the universe had a beginning and will have an ending it implies that there is something else that exists besides our universe that we can observe.

A purely material naturalistic world view ( material realism) demands that something material must be eternal. The evidence of an accelerating expansion has given rise to multi universe theories. Universes that are outside of our universe and can not be observed.

The accelerating expansion of the universe has given support for the theistic views that something besides material realism exists

The universe is expanding at an accelerating rate—or is it?

This is the "South Pillar" region of the star-forming region called the Carina Nebula. Like cracking open a watermelon and finding its seeds, the infrared telescope "busted open" this murky cloud to reveal star embryos tucked inside finger-like pillars of thick dust. Credit: NASA

Five years ago, the Nobel Prize in Physics was awarded to three astronomers for their discovery, in the late 1990s, that the universe is expanding at an accelerating pace.

Their conclusions were based on analysis of Type Ia supernovae - the spectacular thermonuclear explosion of dying stars - picked up by the Hubble space telescope and large ground-based telescopes. It led to the widespread acceptance of the idea that the universe is dominated by a mysterious substance named 'dark energy' that drives this accelerating expansion.

Now, a team of scientists led by Professor Subir Sarkar of Oxford University's Department of Physics has cast doubt on this standard cosmological concept. Making use of a vastly increased data set - a catalogue of 740 Type Ia supernovae, more than ten times the original sample size - the researchers have found that the evidence for acceleration may be flimsier than previously thought, with the data being consistent with a constant rate of expansion.

The study is published in the Nature journal Scientific Reports.

Professor Sarkar, who also holds a position at the Niels Bohr Institute in Copenhagen, said: 'The discovery of the accelerating expansion of the universe won the Nobel Prize, the Gruber Cosmology Prize, and the Breakthrough Prize in Fundamental Physics. It led to the widespread acceptance of the idea that the universe is dominated by "dark energy" that behaves like a cosmological constant - this is now the "standard model" of cosmology.

'However, there now exists a much bigger database of supernovae on which to perform rigorous and detailed statistical analyses. We analysed the latest catalogue of 740 Type Ia supernovae - over ten times bigger than the original samples on which the discovery claim was based - and found that the evidence for accelerated expansion is, at most, what physicists call "3 sigma". This is far short of the "5 sigma" standard required to claim a discovery of fundamental significance.

'An analogous example in this context would be the recent suggestion for a new particle weighing 750 GeV based on data from the Large Hadron Collider at CERN. It initially had even higher significance - 3.9 and 3.4 sigma in December last year - and stimulated over 500 theoretical papers. However, it was announced in August that new data show that the significance has dropped to less than 1 sigma. It was just a statistical fluctuation, and there is no such particle.'

There is other data available that appears to support the idea of an accelerating universe, such as information on the cosmic microwave background - the faint afterglow of the Big Bang - from the Planck satellite. However, Professor Sarkar said: 'All of these tests are indirect, carried out in the framework of an assumed model, and the cosmic microwave background is not directly affected by dark energy. Actually, there is indeed a subtle effect, the late-integrated Sachs-Wolfe effect, but this has not been convincingly detected.

'So it is quite possible that we are being misled and that the apparent manifestation of dark energy is a consequence of analysing the data in an oversimplified theoretical model - one that was in fact constructed in the 1930s, long before there was any real data. A more sophisticated theoretical framework accounting for the observation that the universe is not exactly homogeneous and that its matter content may not behave as an ideal gas - two key assumptions of standard cosmology - may well be able to account for all observations without requiring dark energy. Indeed, vacuum energy is something of which we have absolutely no understanding in fundamental theory.'

Professor Sarkar added: 'Naturally, a lot of work will be necessary to convince the physics community of this, but our work serves to demonstrate that a key pillar of the standard cosmological model is rather shaky. Hopefully this will motivate better analyses of cosmological data, as well as inspiring theorists to investigate more nuanced cosmological models. Significant progress will be made when the European Extremely Large Telescope makes observations with an ultrasensitive "laser comb" to directly measure over a ten to 15-year period whether the expansion rate is indeed accelerating.'

Solving one of nature's great puzzles: What drives the accelerating expansion of the universe?

UBC physicists may have solved one of nature's great puzzles: what causes the accelerating expansion of our universe?

PhD student Qingdi Wang has tackled this question in a new study that tries to resolve a major incompatibility issue between two of the most successful theories that explain how our universe works: quantum mechanics and Einstein's theory of general relativity.

The study suggests that if we zoomed in-way in-on the universe, we would realize it's made up of constantly fluctuating space and time.

"Space-time is not as static as it appears, it's constantly moving," said Wang.

"This is a new idea in a field where there hasn't been a lot of new ideas that try to address this issue," said Bill Unruh, a physics and astronomy professor who supervised Wang's work.

In 1998, astronomers found that our universe is expanding at an ever-increasing rate, implying that space is not empty and is instead filled with dark energy that pushes matter away.

The most natural candidate for dark energy is vacuum energy. When physicists apply the theory of quantum mechanics to vacuum energy, it predicts that there would be an incredibly large density of vacuum energy, far more than the total energy of all the particles in the universe. If this is true, Einstein's theory of general relativity suggests that the energy would have a strong gravitational effect and most physicists think this would cause the universe to explode.

Fortunately, this doesn't happen and the universe expands very slowly. But it is a problem that must be resolved for fundamental physics to progress.

Unlike other scientists who have tried to modify the theories of quantum mechanics or general relativity to resolve the issue, Wang and his colleagues Unruh and Zhen Zhu, also a UBC PhD student, suggest a different approach. They take the large density of vacuum energy predicted by quantum mechanics seriously and find that there is important information about vacuum energy that was missing in previous calculations.

Their calculations provide a completely different physical picture of the universe. In this new picture, the space we live in is fluctuating wildly. At each point, it oscillates between expansion and contraction. As it swings back and forth, the two almost cancel each other but a very small net effect drives the universe to expand slowly at an accelerating rate.

But if space and time are fluctuating, why can't we feel it?

"This happens at very tiny scales, billions and billions times smaller even than an electron," said Wang.

"It's similar to the waves we see on the ocean," said Unruh. "They are not affected by the intense dance of the individual atoms that make up the water on which those waves ride."

Explaining the accelerating expansion of the universe without dark energy

Enigmatic dark energy, thought to make up 68% of the universe, may not exist at all, according to a Hungarian-American team. The researchers believe that standard models of the universe fail to take account of its changing structure, but that once this is done the need for dark energy disappears. The team publish their results in a paper in Monthly Notices of the Royal Astronomical Society.

Our universe was formed in the Big Bang, 13.8 billion years ago, and has been expanding ever since. The key piece of evidence for this expansion is Hubble's law, based on observations of galaxies, which states that on average, the speed with which a galaxy moves away from us is proportional to its distance.

Astronomers measure this velocity of recession by looking at lines in the spectrum of a galaxy, which shift more towards red the faster the galaxy is moving away. From the 1920s, mapping the velocities of galaxies led scientists to conclude that the whole universe is expanding, and that it began life as a vanishingly small point.

In the second half of the twentieth century, astronomers found evidence for unseen 'dark' matter by observing that something extra was needed to explain the motion of stars within galaxies. Dark matter is now thought to make up 27% of the content of universe (in contrast 'ordinary' matter amounts to only 5%).

Observations of the explosions of white dwarf stars in binary systems, so-called Type Ia supernovae, in the 1990s then led scientists to the conclusion that a third component, dark energy, made up 68% of the cosmos, and is responsible for driving an acceleration in the expansion of the universe.

In the new work, the researchers, led by PhD student Gábor Rácz of Eötvös Loránd University in Hungary, question the existence of dark energy and suggest an alternative explanation. They argue that conventional models of cosmology (the study of the origin and evolution of the universe), rely on approximations that ignore its structure, and where matter is assumed to have a uniform density.

"Einstein's equations of general relativity that describe the expansion of the universe are so complex mathematically that for a hundred years no solutions accounting for the effect of cosmic structures have been found. We know from very precise supernova observations that the universe is accelerating, but at the same time we rely on coarse approximations to Einstein's equations which may introduce serious side-effects, such as the need for dark energy, in the models designed to fit the observational data." explains Dr László Dobos, co-author of the paper, also at Eötvös Loránd University.

In practice, normal and dark matter appear to fill the universe with a foam-like structure, where galaxies are located on the thin walls between bubbles, and are grouped into superclusters. The insides of the bubbles are in contrast almost empty of both kinds of matter.

Using a computer simulation to model the effect of gravity on the distribution of millions of particles of dark matter, the scientists reconstructed the evolution of the universe, including the early clumping of matter, and the formation of large scale structure.

Unlike conventional simulations with a smoothly expanding universe, taking the structure into account led to a model where different regions of the cosmos expand at different rate. The average expansion rate though is consistent with present observations, which suggest an overall acceleration.

Dr Dobos adds: "The theory of general relativity is fundamental in understanding the way the universe evolves. We do not question its validity we question the validity of the approximate solutions. Our findings rely on a mathematical conjecture which permits the differential expansion of space, consistent with general relativity, and they show how the formation of complex structures of matter affects the expansion. These issues were previously swept under the rug but taking them into account can explain the acceleration without the need for dark energy."

If this finding is upheld, it could have a significant impact on models of the universe and the direction of research in physics. For the past 20 years, astronomers and theoretical physicists have speculated on the nature of dark energy, but it remains an unsolved mystery. With the new model, the team expect at the very least to start a lively debate.

Press release

“Some say the world will end in fire, some say in ice…” *
What will be the final destiny of the Universe? Probably it will end in ice, if we are to believe this year’s Nobel Laureates in Physics. They have studied several dozen exploding stars, called supernovae, and discovered that the Universe is expanding at an ever-accelerating rate. The discovery came as a complete surprise even to the Laureates themselves.

In 1998, cosmology was shaken at its foundations as two research teams presented their findings. Headed by Saul Perlmutter, one of the teams had set to work in 1988. Brian Schmidt headed another team, launched at the end of 1994, where Adam Riess was to play a crucial role.

The research teams raced to map the Universe by locating the most distant supernovae. More sophisticated telescopes on the ground and in space, as well as more powerful computers and new digital imaging sensors (CCD, Nobel Prize in Physics in 2009), opened the possibility in the 1990s to add more pieces to the cosmological puzzle.

The teams used a particular kind of supernova, called type Ia supernova. It is an explosion of an old compact star that is as heavy as the Sun but as small as the Earth. A single such supernova can emit as much light as a whole galaxy. All in all, the two research teams found over 50 distant supernovae whose light was weaker than expected – this was a sign that the expansion of the Universe was accelerating. The potential pitfalls had been numerous, and the scientists found reassurance in the fact that both groups had reached the same astonishing conclusion.

For almost a century, the Universe has been known to be expanding as a consequence of the Big Bang about 14 billion years ago. However, the discovery that this expansion is accelerating is astounding. If the expansion will continue to speed up the Universe will end in ice.

The acceleration is thought to be driven by dark energy, but what that dark energy is remains an enigma – perhaps the greatest in physics today. What is known is that dark energy constitutes about three quarters of the Universe. Therefore the findings of the 2011 Nobel Laureates in Physics have helped to unveil a Universe that to a large extent is unknown to science. And everything is possible again.

Read more about this year’s prize

Saul Perlmutter, U.S. citizen. Born 1959 in Champaign-Urbana, IL, USA. Ph.D. 1986 from University of California, Berkeley, USA. Head of the Supernova Cosmology Project, Professor of Astrophysics, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA.

Brian P. Schmidt, U.S. and Australian citizen. Born 1967 in Missoula, MT, USA. Ph.D. 1993 from Harvard University, Cambridge, MA, USA. Head of the High-z Supernova Search Team, Distinguished Professor, Australian National University, Weston Creek, Australia.

Adam G. Riess, U.S. citizen. Born 1969 in Washington, DC, USA. Ph.D. 1996 from Harvard University, Cambridge, MA, USA. Professor of Astronomy and Physics, Johns Hopkins University and Space Telescope Science Institute, Baltimore, MD, USA.

Prize amount: SEK 10 million, with one half to Saul Perlmutter and the other half to be shared equally between Brian Schmidt and Adam Riess.

Contact persons: Erik Huss, Press Officer, Phone +46 8 673 95 44, mobile +46 70 673 96 50, [email protected]
Annika Moberg, Editor, Phone +46 8 673 95 22, Mobile +46 70 673 96 90, [email protected]

* Robert Frost, Fire and Ice, 1920

Nobel Prize® is a registered trademark of the Nobel Foundation.

The Royal Swedish Academy of Sciences, founded in 1739, is an independent organization whose overall objective is to promote the sciences and strengthen their influence in society. The Academy takes special responsibility for the natural sciences and mathematics, but endeavours to promote the exchange of ideas between various disciplines.

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Nobel Prizes 2020

Twelve laureates were awarded a Nobel Prize in 2020, for achievements that have conferred the greatest benefit to humankind.

Their work and discoveries range from the formation of black holes and genetic scissors to efforts to combat hunger and develop new auction formats.

Hubble confirms cosmic acceleration with weak lensing

A new study led by European scientists presents the most comprehensive analysis of data from the most ambitious survey ever undertaken by the NASA/ESA Hubble Space Telescope. These researchers have, for the first time ever, used Hubble data to probe the effects of the natural gravitational "weak lenses" in space and characterise the expansion of the Universe.

A group of astronomers [1], led by Tim Schrabback of the Leiden Observatory, conducted an intensive study of over 446 000 galaxies within the COSMOS field, the result of the largest survey ever conducted with Hubble. In making the COSMOS survey, Hubble photographed 575 slightly overlapping views of the same part of the Universe using the Advanced Camera for Surveys (ACS) onboard Hubble. It took nearly 1000 hours of observations.

In addition to the Hubble data, researchers used redshift [2] data from ground-based telescopes to assign distances to 194 000 of the galaxies surveyed (out to a redshift of 5). "The sheer number of galaxies included in this type of analysis is unprecedented, but more important is the wealth of information we could obtain about the invisible structures in the Universe from this exceptional dataset," says co-author Patrick Simon from Edinburgh University.

In particular, the astronomers could "weigh" the large-scale matter distribution in space over large distances. To do this, they made use of the fact that this information is encoded in the distorted shapes of distant galaxies, a phenomenon referred to as weak gravitational lensing [3]. Using complex algorithms, the team led by Schrabback has improved the standard method and obtained galaxy shape measurements to an unprecedented precision. The results of the study will be published in an upcoming issue of Astronomy and Astrophysics.

The meticulousness and scale of this study enables an independent confirmation that the expansion of the Universe is accelerated by an additional, mysterious component named dark energy. A handful of other such independent confirmations exist. Scientists need to know how the formation of clumps of matter evolved in the history of the Universe to determine how the gravitational force, which holds matter together, and dark energy, which pulls it apart by accelerating the expansion of the Universe, have affected them. "Dark energy affects our measurements for two reasons. First, when it is present, galaxy clusters grow more slowly, and secondly, it changes the way the Universe expands, leading to more distant — and more efficiently lensed — galaxies. Our analysis is sensitive to both effects," says co-author Benjamin Joachimi from the University of Bonn. "Our study also provides an additional confirmation for Einstein's theory of general relativity, which predicts how the lensing signal depends on redshift," adds co-investigator Martin Kilbinger from the Institut d'Astrophysique de Paris and the Excellence Cluster Universe.

The large number of galaxies included in this study, along with information on their redshifts is leading to a clearer map of how, exactly, part of the Universe is laid out it helps us see its galactic inhabitants and how they are distributed. "With more accurate information about the distances to the galaxies, we can measure the distribution of the matter between them and us more accurately," notes co-investigator Jan Hartlap from the University of Bonn. "Before, most of the studies were done in 2D, like taking a chest X-ray. Our study is more like a 3D reconstruction of the skeleton from a CT scan. On top of that, we are able to watch the skeleton of dark matter mature from the Universe's youth to the present," comments William High from Harvard University, another co-author.

The astronomers specifically chose the COSMOS survey because it is thought to be a representative sample of the Universe. With thorough studies such as the one led by Schrabback, astronomers will one day be able to apply their technique to wider areas of the sky, forming a clearer picture of what is truly out there.


The Hubble Space Telescope is a project of international cooperation between ESA and NASA.

[1] The international team of astronomers in this study was led by Tim Schrabback of the Leiden University. Other collaborators included: J. Hartlap (University of Bonn), B. Joachimi (University of Bonn), M. Kilbinger (IAP), P. Simon (University of Edinburgh), K. Benabed (IAP), M. Bradac (UCDavis), T. Eifler (University of Bonn), T. Erben (University of Bonn), C. Fassnacht (University of California, Davis), F. W. High(Harvard), S. Hilbert (MPA), H. Hildebrandt (Leiden Observatory), H. Hoekstra (Leiden Observatory), K. Kuijken (Leiden Observatory), P. Marshall (KIPAC), Y. Mellier (IAP), E. Morganson (KIPAC), P. Schneider (University of Bonn), E. Semboloni (University of Bonn), L. Van Waerbeke (UBC) and M. Velander (Leiden Observatory).

[2] In astronomy, the redshift denotes the fraction by which the lines in the spectrum of an object are shifted towards longer wavelengths due to the expansion of the Universe. The observed redshift of a remote galaxy provides an estimate of its distance. In this study the researchers used redshift information computed by the COSMOS team, who also obtained the HST data (PI: N. Scoville, 38S), based on observations from the SUBARU, CFHT, UKIRT, Spitzer, GALEX, NOAO, VLT, and Keck telescopes ( 690.1236I).

[3]Weak gravitational lensing: The phenomenon of gravitational lensing is the warping of spacetime by the gravitational field of a concentration of matter, such as a galaxy cluster. When light rays from distant background galaxies pass this matter concentration, their path is bent and the galaxy images are distorted. In the case of weak lensing, these distortions are small, and must be measured statistically. This analysis provides a direct estimate for the strength of the gravitational field, and therefore the mass of the matter concentration. When determining precise shapes of galaxies, astronomers have to deal with three main factors: the intrinsic shape of the galaxy (which is unknown), the gravitational lensing effect they want to measure, and systematic effects caused by the telescope and camera, as well as the atmosphere, in case of ground-based observations.

Image credit: NASA, ESA, P. Simon (University of Bonn) and T. Schrabback (Leiden Observatory)

How Long Has The Universe Been Accelerating?

Perhaps the biggest discovery about the Universe in the last generation came at the very end of the 20th century, when we uncovered one of the most disconcerting cosmic truths: the distant galaxies, as time goes on, aren't just receding from us, they're speeding up as they move away from us. The discovery of the accelerated expansion of the Universe, by the Supernova Cosmology Project and the High-z Supernova Search Team, was awarded the 2011 Nobel Prize in Physics, but is one of the most bizarre and unexplained phenomena in the Universe. The thing is, the Universe wasn't always accelerating away from us like this. For billions of years, the expansion was slowing down, and to someone alive ten billion years ago, it might have looked like it could recollapse. Let's take a look at what happened, and how we know.

Image credit: Miguel Quartin, Valerio Marra and Luca Amendola, Phys. Rev. D, via . [+]

In the 1920s, four pieces of evidence -- three observational and one theoretical -- combined to teach us that the Universe was expanding. They were:

This led to a picture of the Universe as early as 1929 where the Universe was hotter, denser, and expanding more rapidly in the past, and was getting cooler, less dense, and where the expansion rate was slowing down as time went on.

Image credit: ESA/Hubble & NASA, of galaxy cluster LCDS-0829.

This makes sense, if you think about it in the context of the Big Bang. Imagine the Big Bang as the starting gun of a great cosmic race, a race between the initial expansion on one hand, which starts off incredibly rapid, and between gravitation on the other hand, which works to pull everything back together. You can easily imagine three different possibilities, each of which results in a different fate for the Universe:

  • A Big Crunch.Perhaps the initial expansion rate is fast, but over time, the force that gravity exerts turns out to be stronger. The expansion rate would slow down and then cease. The Universe would reach a maximum size and then begin contracting. And finally, it would recollapse, imploding in a state that was essentially the Big Bang in reverse.
  • A Big Freeze. This is the opposite scenario: where the expansion starts off fast, and gravity works to slow it down, but is insufficient. The expansion continues at a rapid rate for all eternity, with gravity working to slow it down the whole time, but never succeeding in bringing it to a stop. This scenario is known as the heat death of the Universe, or the Big Freeze.
  • A Critical Universe. There's also the possibility that you're right on the edge of the two, where the expansion rate and gravity balance each other perfectly, and the expansion rate slows over time and asymptotes towards zero. If there were just one more or one fewer particle in the Universe, you’d get either the first or second scenario above instead, but that particle isn't there. This "critical Universe" scenario results in the slowest possible heat death imaginable.

For billions of years, it looked like the critical case was going to win. You see, when you live in the Universe and look out at the different galaxies, you can measure not only what the expansion rate is today, but by looking at the more distant galaxies, you can measure what the expansion rate used to be earlier in the Universe's history.

Image credit: NASA, ESA, and Z. Levay (STScI). The GOODS-North survey, shown here, contains some of . [+] the most distant galaxies ever observed, a great many of which are already unreachable by us.

So for billions of years -- about seven billion, to be more precise -- it looked like we lived in a critical Universe. The expansion began dominated by radiation (photons and neutrinos), and then it cooled enough that matter (both normal and dark matter, combined) became dominant. As the Universe continued to expand, the matter density dropped and dropped, since matter density is just mass (which is a constant) over volume (which is increasing).

But at some point, the matter density dropped to such a low value that another, more subtle contribution to the Universe's energy density began to show up: dark energy. At around seven billion years of age, dark energy's value reached a few percent that of the total energy density, and by time the Universe was 7.8 billion years old, the dark energy density reached a very important value: 33% of the total energy density in the Universe. That's an important value, because that's the amount of dark energy necessary -- in a Universe otherwise filled with matter -- to cause the expansion rate to begin accelerating!

Image credit: NASA & ESA, via

Since that time, some 6 billion years ago, the matter density has continued to drop, while dark energy has remained a constant. At present, dark energy makes up some 68% of the total energy in the Universe, with matter having dropped to be about 32% total (27% dark matter and 5% normal matter). As time goes on in the future, the matter density will continue to drop, while the dark energy density will remain constant, meaning dark energy becomes more and more dominant.

Image credit: E. Siegel, of the various energy density fractions that the Universe is composed of at . [+] various points in its past.

For individual galaxies, that means that a galaxy that began receding from us quickly at the moment of the Big Bang would have seen its apparent recession speed slow down from our perspective for the first 7.8 billion years. At that moment, the recession speed would have stopped slowing, and would have remained constant for a brief while. And ever since then, it would have sped up, receding ever faster as the space between ourselves and the distant galaxies expands at an ever increasing rate. At some point -- and frighteningly, this is already true for 97% of the galaxies in our visible Universe -- each and every galaxy beyond our local group will appear to recede at a speed greater than the speed of light, making it forever unreachable by us due to the limitations of physics.

Image credit: E. Siegel, based on work by Wikimedia Commons users Azcolvin 429 and Frédéric . [+] MICHEL.

The Universe has always, as far as we can tell, had the amount of dark energy it has today inherent to space itself. But it took 7.8 billion years, or the entire Universe's history up until about 1.5 billion years before our Solar System formed, for the matter density to drop to such a point that dark energy came to dominate the Universe's expansion. Ever since then, all the galaxies beyond our local group have been accelerating away from us, and will continue to do so until the very last one is gone. The Universe has been accelerating for the past six billion years, and if we had come along sooner than that, we might never have considered an option beyond the three possibilities our intuition would have led us to. Instead, we get to perceive and draw conclusions about the Universe exactly as it is, and that's perhaps the greatest reward of all.

Cosmologists Present Explanation For Accelerating Expansion Of The Universe

Why is the universe expanding at an accelerating rate, spreading its contents over ever greater dimensions of space? An original solution to this puzzle, certainly the most fascinating question in modern cosmology, has been put forward by four theoretical physicists, Edward W. Kolb of the U.S. Department of Energy's Fermi National Accelerator Laboratory, Chicago (USA): Sabino Matarrese of the University of Padova Alessio Notari from the University of Montreal (Canada) and Antonio Riotto of INFN (Istituto Nazionale di Fisica Nucleare) of Padova (Italy). Their study has been submitted to the journal Physical Review Letters.

Over the last hundred years, the expansion of the universe has been a subject of passionate discussion, engaging the most brilliant minds of the century. Like his contemporaries, Albert Einstein initially thought that the universe was static: that it neither expanded nor shrank. When his own Theory of General Relativity clearly showed that the universe should expand or contract, Einstein chose to introduce a new ingredient into his theory. His "cosmological constant" represented a mass density of empty space that drove the universe to expand at an ever-increasing rate.

When in 1929 Edwin Hubble proved that the universe is in fact expanding, Einstein repudiated his cosmological constant, calling it "the greatest blunder of my life." Then, almost a century later, physicists resurrected the cosmological constant in a variant called dark energy. In 1998, observations of very distant supernovae demonstrated that the universe is expanding at an accelerating rate. This accelerating expansion seemed to be explicable only by the presence of a new component of the universe, a "dark energy," representing some 70 percent of the total mass of the universe. Of the rest, about 25 percent appears to be in the form of another mysterious component, dark matter while only about 5 percent comprises ordinary matter, those quarks, protons, neutrons and electrons that we and the galaxies are made of.

"The hypothesis of dark energy is extremely fascinating," explains Padova's Antonio Riotto, "but on the other hand it represents a serious problem. No theoretical model, not even the most modern, such as supersymmetry or string theory, is able to explain the presence of this mysterious dark energy in the amount that our observations require. If dark energy were the size that theories predict, the universe would have expanded with such a fantastic velocity that it would have prevented the existence of everything we know in our cosmos."

The requisite amount of dark energy is so difficult to reconcile with the known laws of nature that physicists have proposed all manner of exotic explanations, including new forces, new dimensions of spacetime, and new ultralight elementary particles. However, the new report proposes no new ingredient for the universe, only a realization that the present acceleration of the universe is a consequence of the standard cosmological model for the early universe: inflation.

"Our solution to the paradox posed by the accelerating universe," Riotto says, "relies on the so-called inflationary theory, born in 1981. According to this theory, within a tiny fraction of a second after the Big Bang, the universe experienced an incredibly rapid expansion. This explains why our universe seems to be very homogeneous. Recently, the Boomerang and WMAP experiments, which measured the small fluctuations in the background radiation originating with the Big Bang, confirmed inflationary theory.

It is widely believed that during the inflationary expansion early in the history of the universe, very tiny ripples in spacetime were generated, as predicted by Einstein's theory of General Relativity. These ripples were stretched by the expansion of the universe and extend today far beyond our cosmic horizon, that is over a region much bigger than the observable universe, a distance of about 15 billion light years. In their current paper, the authors propose that it is the evolution of these cosmic ripples that increases the observed expansion of the universe and accounts for its acceleration.

"We realized that you simply need to add this new key ingredient, the ripples of spacetime generated during the epoch of inflation, to Einstein's General Relativity to explain why the universe is accelerating today," Riotto says. "It seems that the solution to the puzzle of acceleration involves the universe beyond our cosmic horizon. No mysterious dark energy is required."

Fermilab's Kolb called the authors' proposal the most conservative explanation for the accelerating universe. "It requires only a proper accounting of the physical effects of the ripples beyond our cosmic horizon," he said.

Data from upcoming experiments will allow cosmologists to test the proposal. "Whether Einstein was right when he first introduced the cosmological constant, or whether he was right when he later refuted the idea will soon be tested by a new round of precision cosmological observations," Kolb said. "New data will soon allow us to distinguish between our explanation for the accelerated expansion of the universe and the dark energy solution."

INFN (Istituto Nazionale di Fisica Nucleare), Italy's national nuclear physics institute, supports, coordinates and carries out scientific research in subnuclear, nuclear and astroparticle physics and is involved in developing relevant technologies.

Fermilab, in Batavia, Illinois, USA, is operated by Universities Research Association, Inc. for the Department of Energy's Office of Science, which funds advanced research in particle physics and cosmology.