Accelerating expansion of the universe

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The accelerating expansion of the universe is the observation that the universe appears to be expanding at an increasing rate,[1] so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.[2]

The accelerated expansion was discovered in 1998, by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration.[3][4][5] The idea was that these type 1a supernovae all have almost the same intrinsic brightness (a standard candle). Since objects that are further away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The distance can then be compared to the supernovae's redshift, which measures how fast the supernovae are receding from us.[6] The result was that the universe is expanding at an accelerating rate. This was unexpected, and cosmologists at the time expected that the expansion would be decelerating due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery.[7] Confirmatory evidence has been found in baryon acoustic oscillations and in analyses of the clustering of galaxies.

The expansion of the universe is thought to have been accelerating since the universe entered its dark-energy-dominated era roughly 5 billion years ago.[8][notes 1] Within the framework of general relativity, an accelerating expansion can be accounted for by a positive value of the cosmological constant Λ, equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive Λ) is used in the current standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.


In the decades since the detection of cosmic microwave background (CMB) in 1965,[9] the Big Bang model has become the most accepted model explaining the evolution of our universe. The Friedmann equation defines how the energy in the universe drives its expansion.

where Κ represents the curvature of the universe, a(t) is the scale factor, ρ is the total energy density of the universe, and H is the Hubble parameter.[10]

We define a critical density

and the density parameter

We can then rewrite the Hubble parameter as

where the four currently hypothesized contributors to the energy density of the universe are curvature, matter, radiation and dark energy.[11] Each of the components decreases with the expansion of the universe (increasing scale factor), except perhaps the dark energy term. It is the values of these cosmological parameters which physicists use to determine the acceleration of the universe.

The acceleration equation describes the evolution of the scale factor with time

where the pressure P is defined by the cosmological model chosen. (see explanatory models below)

Physicists at one time were so assured of the deceleration of the universe's expansion that they introduced a so-called deceleration parameter q0.[12][page needed] Current observations point towards this deceleration parameter being negative.

Evidence for acceleration[edit]

To learn about the rate of expansion of the universe we look at the magnitude-redshift relationship of astronomical objects using standard candles, or their distance-redshift relationship using standard rulers. We can also look at the growth of large-scale structure, and find that the observed values of the cosmological parameters are best described by models which include an accelerating expansion.

Supernova observation[edit]

Artist's impression of a Type Ia supernova, as revealed by spectro-polarimetry observations

The first evidence for acceleration came from the observation of Type Ia supernovae, which are exploding white dwarfs that have exceeded their stability limit. Because they all have similar masses, their intrinsic luminosity is standardizable. Repeated imaging of selected areas of the sky is used to discover the supernovae, then follow-up observations give their peak brightness, which is converted into a quantity known as luminosity distance (see distance measures in cosmology for details).[13] Spectral lines of their light can be used to determine their redshift.

For supernovae at redshift less than around 0.1, or light travel time less than 10 percent of the age of the universe, this gives a nearly linear distance–redshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time. The full calculation requires integration of the Friedmann equation, but a simple derivation can be given as follows: the redshift z directly gives the cosmic scale factor at the time the supernova exploded.

So a supernova with a measured redshift z = 0.5 implies the universe was 1/1 + 0.5 = 2/3 of its present size when the supernova exploded. In an accelerating universe, the universe was expanding more slowly in the past than it is today, which means it took a longer time to expand from two thirds its present size to its present size compared to a non-accelerating universe. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations. Adam Riess found that "the distances of the high-redshift SNe Ia were, on average, 10% to 15% farther than expected in a low mass density ΩM = 0.2 universe without a cosmological constant".[14] This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.[15]

Baryon acoustic oscillations[edit]

In the early universe before recombination and decoupling took place, photons and matter existed in a primordial plasma. Points of higher density in the photon-baryon plasma would contract, being compressed by gravity until the pressure became too large and they expanded again.[12][page needed] This contraction and expansion created vibrations in the plasma analogous to sound waves. Since dark matter only interacts gravitationally it stayed at the centre of the sound wave, the origin of the original overdensity. When decoupling occurred, approximately 380,000 years after the Big Bang,[16] photons separated from matter and were able to stream freely through the universe, creating the cosmic microwave background as we know it. This left shells of baryonic matter at a fixed radius from the overdensities of dark matter, a distance known as the sound horizon. As time passed and the universe expanded, it was at these anisotropies of matter density where galaxies started to form. So by looking at the distances at which galaxies at different redshifts tend to cluster, it is possible to determine a standard angular diameter distance and use that to compare to the distances predicted by different cosmological models.

Peaks have been found in the correlation function (the probability that two galaxies will be a certain distance apart) at 100 h−1 Mpc,[11] indicating that this is the size of the sound horizon today, and by comparing this to the sound horizon at the time of decoupling (using the CMB), we can confirm that the expansion of the universe is accelerating.[17]

Clusters of galaxies[edit]

Measuring the mass functions of galaxy clusters, which describe the number density of the clusters above a threshold mass, also provides evidence for dark energy.[18] By comparing these mass functions at high and low redshifts to those predicted by different cosmological models, values for w and Ωm are obtained which confirm a low matter density and a non zero amount of dark energy.[15]

Age of the universe[edit]

Given a cosmological model with certain values of the cosmological density parameters, it is possible to integrate the Friedmann equations and derive the age of the universe.

By comparing this to actual measured values of the cosmological parameters, we can confirm the validity of a model which is accelerating now, and had a slower expansion in the past.[15]

Explanatory models[edit]

The expansion of the Universe accelerating. Time flows from bottom to top

Dark energy[edit]

The most important property of dark energy is that it has negative pressure which is distributed relatively homogeneously in space.

where c is the speed of light and ρ is the energy density. Different theories of dark energy suggest different values of w, with w < −1/3 for cosmic acceleration (this leads to a positive value of ä in the acceleration equation above).

The simplest explanation for dark energy is that it is a cosmological constant or vacuum energy; in this case w = −1. This leads to the Lambda-CDM model, which has generally been known as the Standard Model of Cosmology from 2003 through the present, since it is the simplest model in good agreement with a variety of recent observations. Riess found that their results from supernovae observations favoured expanding models with positive cosmological constant (Ωλ > 0) and a current acceleration of the expansion (q0 < 0).[14]

Phantom energy[edit]

Current observations allow the possibility of a cosmological model containing a dark energy component with equation of state w < −1. This phantom energy density would become infinite in finite time, causing such a huge gravitational repulsion that the universe would lose all structure and end in a Big Rip.[19] For example, for w = −3/2 and H0 = 70 km·s−1·Mpc−1, the time remaining before the universe ends in this "Big Rip" is 22 billion years.[20]

Alternative theories[edit]

There are many alternative explanations for the accelerating universe. Some examples are quintessence, a proposed form of dark energy with a non-constant state equation, whose density decreases with time. Dark fluid is an alternative explanation for accelerating expansion which attempts to unite dark matter and dark energy into a single framework.[21] Alternatively, some authors have argued that the universe expansion acceleration could be due to a repulsive gravitational interaction of antimatter.[22][23][24]

Another type of model, the backreaction conjecture,[25][26] was proposed by cosmologist Syksy Räsänen:[27] the rate of expansion is not homogenous, but we are in a region where expansion is faster than the background. Inhomogeneities in the early universe cause the formation of walls and bubbles, where the inside of a bubble has less matter than on average. According to general relativity, space is less curved than on the walls, and thus appears to have more volume and a higher expansion rate. In the denser regions, the expansion is retarded by a higher gravitational attraction. Therefore, the inward collapse of the denser regions looks the same as an accelerating expansion of the bubbles, leading us to conclude that the universe is expanding at an accelerating rate.[28] The benefit is that it does not require any new physics such as dark energy. Räsänen does not consider the model likely, but without any falsification, it must remain a possibility. It would require rather large density fluctuations (20%) to work.[27]

A final possibility is that dark energy is an illusion caused by some bias in measurements. For example, if we are located in an emptier-than-average region of space, the observed cosmic expansion rate could be mistaken for a variation in time, or acceleration.[29][30][31][32] A different approach uses a cosmological extension of the equivalence principle to show how space might appear to be expanding more rapidly in the voids surrounding our local cluster. While weak, such effects considered cumulatively over billions of years could become significant, creating the illusion of cosmic acceleration, and making it appear as if we live in a Hubble bubble.[33][34][35] Yet other possibilities are that the accelerated expansion of the universe is an illusion caused by the relative motion of us to the rest of the universe,[36][37] or that the supernovae sample size used wasn't large enough.[38][39]

Theories for the consequences to the universe[edit]

As the universe expands, the density of radiation and ordinary dark matter declines more quickly than the density of dark energy (see equation of state) and, eventually, dark energy dominates. Specifically, when the scale of the universe doubles, the density of matter is reduced by a factor of 8, but the density of dark energy is nearly unchanged (it is exactly constant if the dark energy is a cosmological constant).[12][page needed]

In models where dark energy is a cosmological constant, the universe will expand exponentially with time from now on, coming closer and closer to a de Sitter spacetime. This will eventually lead to all evidence for the Big Bang disappearing, as the cosmic microwave background is redshifted to lower intensities and longer wavelengths. Eventually its frequency will be low enough that it will be absorbed by the interstellar medium, and so be screened from any observer within the galaxy. This will occur when the universe is less than 50 times its current age, leading to the end of cosmology as we know it as the distant universe turns dark.[40]

A constantly expanding universe with non-zero cosmological constant has mass density decreasing over time, to an undetermined point when zero matter density is reached. All matter (electrons, protons and neutrons) would ionize and disintegrate, with objects dissipating away.[41]

Alternatives for the ultimate fate of the universe include the Big Rip mentioned above, a Big Bounce, Big Freeze, Big Crunch or possible proton decay.

See also[edit]


  1. ^ [8] Frieman, Turner & Huterer (2008) p. 6: "The Universe has gone through three distinct eras: radiation-dominated, z ≳ 3000; matter-dominated, 3000 ≳ z ≳ 0.5; and dark-energy-dominated, z ≲ 0.5. The evolution of the scale factor is controlled by the dominant energy form: a(t) ∝ t2/3(1 + w) (for constant w). During the radiation-dominated era, a(t) ∝ t1/2; during the matter-dominated era, a(t) ∝ t2/3; and for the dark energy-dominated era, assuming w = −1, asymptotically a(t) ∝ exp(Ht)."
    p. 44: "Taken together, all the current data provide strong evidence for the existence of dark energy; they constrain the fraction of critical density contributed by dark energy, 0.76 ± 0.02, and the equation-of-state parameter, w ≈ −1 ± 0.1 (stat) ± 0.1 (sys), assuming that w is constant. This implies that the Universe began accelerating at redshift z 0.4 and age t 10 Gyr. These results are robust – data from any one method can be removed without compromising the constraints – and they are not substantially weakened by dropping the assumption of spatial flatness."


  1. ^ Overbye, Dennis (20 February 2017). "Cosmos Controversy: The Universe Is Expanding, but How Fast?". New York Times. Retrieved 21 February 2017. 
  2. ^ "Is the universe expanding faster than the speed of light?". 
  3. ^ "Nobel physics prize honours accelerating universe find". BBC News. 2011-10-04. 
  4. ^ "The Nobel Prize in Physics 2011". Retrieved 2011-10-06. 
  5. ^ Peebles, P. J. E.; Ratra, Bharat (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75 (2): 559–606. Bibcode:2003RvMP...75..559P. arXiv:astro-ph/0207347Freely accessible. doi:10.1103/RevModPhys.75.559. 
  6. ^ See also Hubble law, which established that the further an object is from us, the faster it is receding.
  7. ^ Weinberg, Steven (2008). Cosmology. Oxford University Press. ISBN 9780198526827. 
  8. ^ a b Frieman, Joshua A.; Turner, Michael S.; Huterer, Dragan (2008-01-01). "Dark Energy and the Accelerating Universe". Annual Review of Astronomy and Astrophysics. 46 (1): 385–432. Bibcode:2008ARA&A..46..385F. arXiv:0803.0982Freely accessible. doi:10.1146/annurev.astro.46.060407.145243. 
  9. ^ Penzias, A. A.; Wilson, R. W. (1965). "A Measurement of Excess Antenna Temperature at 4080 Mc/s". The Astrophysical Journal. 142 (1): 419–421. Bibcode:1965ApJ...142..419P. doi:10.1086/148307. 
  10. ^ Nemiroff, Robert J.; Patla, Bijunath. "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265. Bibcode:2008AmJPh..76..265N. arXiv:astro-ph/0703739Freely accessible. doi:10.1119/1.2830536. 
  11. ^ a b Lapuente, P. (2010). "Baryon Acoustic Oscillations". Dark Energy: Observational and Theoretical Approaches. Cambridge, UK: Cambridge University Press. ISBN 978-0521518888. 
  12. ^ a b c Ryden, Barbara (2003). Introduction to Cosmology. San Francisco, CA: Addison Wesley. ISBN 978-0-8053-8912-8. 
  13. ^ Albrecht, Andreas; Bernstein, Gary; Cahn, Robert; Freedman, Wendy L.; Hewitt, Jacqueline; Hu, Wayne; Huth, John; Kamionkowski, Marc; Kolb, Edward W.; Knox, Lloyd; Mather, John C.; Staggs, Suzanne; Suntzeff, Nicholas B. (2006-09-20). "Report of the Dark Energy Task Force". arXiv:astro-ph/0609591Freely accessible. 
  14. ^ a b Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter; Clocchiatti, Alejandro; Diercks, Alan; Garnavich, Peter M.; Gilliland, Ron L.; Hogan, Craig J.; Jha, Saurabh; Kirshner, Robert P.; Leibundgut, B.; Phillips, M. M.; Reiss, David; Schmidt, Brian P.; Schommer, Robert A.; Smith, R. Chris; Spyromilio, J.; Stubbs, Christopher; Suntzeff, Nicholas B.; Tonry, John. "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant". The Astronomical Journal. 116 (3): 1009–1038. Bibcode:1998AJ....116.1009R. arXiv:astro-ph/9805201Freely accessible. doi:10.1086/300499. 
  15. ^ a b c Pain, Reynald; Astier, Pierre (2012). "Observational evidence of the accelerated expansion of the Universe". Comptes Rendus Physique. 13 (6): 521–538. Bibcode:2012CRPhy..13..521A. arXiv:1204.5493Freely accessible. doi:10.1016/j.crhy.2012.04.009. 
  16. ^ Hinshaw, G. (2014). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results". Astrophysical Journal Supplement. 180: 225–245. Bibcode:2009ApJS..180..225H. arXiv:0803.0732Freely accessible. doi:10.1088/0067-0049/180/2/225. 
  17. ^ Eisenstein, Daniel J.; Zehavi, Idit; Hogg, David W.; Scoccimarro, Roman; Blanton, Michael R.; Nichol, Robert C.; Scranton, Ryan; Seo, Hee‐Jong; Tegmark, Max; Zheng, Zheng; Anderson, Scott F.; Annis, Jim; Bahcall, Neta; Brinkmann, Jon; Burles, Scott; Castander, Francisco J.; Connolly, Andrew; Csabai, Istvan; Doi, Mamoru; Fukugita, Masataka; Frieman, Joshua A.; Glazebrook, Karl; Gunn, James E.; Hendry, John S.; Hennessy, Gregory; Ivezić, Zeljko; Kent, Stephen; Knapp, Gillian R.; Lin, Huan; Loh, Yeong‐Shang; Lupton, Robert H.; Margon, Bruce; McKay, Timothy A.; Meiksin, Avery; Munn, Jeffery A.; Pope, Adrian; Richmond, Michael W.; Schlegel, David; Schneider, Donald P.; Shimasaku, Kazuhiro; Stoughton, Christopher; Strauss, Michael A.; SubbaRao, Mark; Szalay, Alexander S.; Szapudi, Istvan; Tucker, Douglas L.; Yanny, Brian; York, Donald G. (2005-11-10). "Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies". The Astrophysical Journal. 633 (2): 560–574. Bibcode:2005ApJ...633..560E. arXiv:astro-ph/0501171Freely accessible. doi:10.1086/466512. 
  18. ^ Dekel, Avishai (1999). Formation of Structure in the Universe. New York, NY: Cambridge University Press. ISBN 9780521586320. 
  19. ^ Caldwell, Robert; Kamionkowski, Marc; Weinberg, Nevin (August 2003). "Phantom Energy: Dark Energy with w < −1 Causes a Cosmic Doomsday". Physical Review Letters. 91 (7): 071301. Bibcode:2003PhRvL..91g1301C. PMID 12935004. arXiv:astro-ph/0302506Freely accessible. doi:10.1103/PhysRevLett.91.071301. 
  20. ^ Caldwell, R. R. (2002). "A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state". Physics Letters B. 545 (1–2): 23–29. Bibcode:2002PhLB..545...23C. arXiv:astro-ph/9908168Freely accessible. doi:10.1016/S0370-2693(02)02589-3. 
  21. ^ Halle, Anaelle; Zhao, Hongsheng; Li, Baojiu (2008). "=Perturbations in a non-uniform dark energy fluid: equations reveal effects of modified gravity and dark matter". Astrophysical Journal Supplement Series. 177 (1). Bibcode:2008ApJS..177....1H. arXiv:0711.0958Freely accessible. doi:10.1086/587744. 
  22. ^ Benoit-Lévy, A.; Chardin, G. (2012). "Introducing the Dirac–Milne universe". Astronomy and Astrophysics. 537: A78. Bibcode:2012A&A...537A..78B. arXiv:1110.3054Freely accessible. doi:10.1051/0004-6361/201016103. open access publication – free to read
  23. ^ Hajduković, D. S. (2012). "Quantum vacuum and virtual gravitational dipoles: the solution to the dark energy problem?". Astrophysics and Space Science. 339 (1): 1–5. Bibcode:2012Ap&SS.339....1H. arXiv:1201.4594Freely accessible. doi:10.1007/s10509-012-0992-y. 
  24. ^ Villata, M. (2013). "On the nature of dark energy: the lattice Universe". Astrophysics and Space Science. 345: 1. Bibcode:2013Ap&SS.345....1V. arXiv:1302.3515Freely accessible. doi:10.1007/s10509-013-1388-3. 
  25. ^ "Backreaction: directions of progress". Classical and Quantum Gravity. 28: 164008. Bibcode:2011CQGra..28p4008R. arXiv:1102.0408Freely accessible. doi:10.1088/0264-9381/28/16/164008. 
  26. ^ "Backreaction in Late-Time Cosmology". Annual Review of Nuclear and Particle Science. 62: 57–79. Bibcode:2012ARNPS..62...57B. arXiv:1112.5335Freely accessible. doi:10.1146/annurev.nucl.012809.104435. 
  27. ^ a b "Is dark energy an illusion?". New Scientist. 2007. 
  28. ^ "A Cosmic 'Tardis': What the Universe Has In Common with 'Doctor Who'". 
  29. ^ Wiltshire, David L. (2007). "Exact Solution to the Averaging Problem in Cosmology". Physical Review Letters. 99 (25): 251101. Bibcode:2007PhRvL..99y1101W. PMID 18233512. arXiv:0709.0732Freely accessible. doi:10.1103/PhysRevLett.99.251101. 
  30. ^ Ishak, Mustapha; Richardson, James; Garred, David; Whittington, Delilah; Nwankwo, Anthony; Sussman, Roberto (2007). "Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?". Physical Review D. 78 (12): 123531. Bibcode:2008PhRvD..78l3531I. arXiv:0708.2943Freely accessible. doi:10.1103/PhysRevD.78.123531. 
  31. ^ Mattsson, Teppo (2007). "Dark energy as a mirage". Gen. Rel. Grav. 42 (3): 567–599. Bibcode:2010GReGr..42..567M. arXiv:0711.4264Freely accessible. doi:10.1007/s10714-009-0873-z. 
  32. ^ Clifton, Timothy; Ferreira, Pedro (April 2009). "Does Dark Energy Really Exist?". Scientific American. 300 (4): 48–55. Bibcode:2009SciAm.300d..48C. PMID 19363920. doi:10.1038/scientificamerican0409-48. Retrieved April 30, 2009. 
  33. ^ Wiltshire, D. (2008). "Cosmological equivalence principle and the weak-field limit". Physical Review D. 78 (8): 084032. Bibcode:2008PhRvD..78h4032W. arXiv:0809.1183Freely accessible. doi:10.1103/PhysRevD.78.084032. 
  34. ^ Gray, Stuart. "Dark questions remain over dark energy". ABC Science Australia. Retrieved 27 January 2013. 
  35. ^ Merali, Zeeya (March 2012). "Is Einstein's Greatest Work All Wrong—Because He Didn't Go Far Enough?". Discover magazine. Retrieved 27 January 2013. 
  36. ^ Wolchover, Natalie (27 September 2011) 'Accelerating universe' could be just an illusion, MSNBC
  37. ^ Tsagas, Christos G. (2011). "Peculiar motions, accelerated expansion, and the cosmological axis". Physical Review D. 84 (6): 063503. Bibcode:2011PhRvD..84f3503T. arXiv:1107.4045Freely accessible. doi:10.1103/PhysRevD.84.063503. 
  38. ^ J. T. Nielsen, A. Guffanti, S. Sarkar (21 October 2016). "Marginal evidence for cosmic acceleration from Type Ia supernovae". Nature Scientific Reports. 6: 35596. Bibcode:2016NatSR...635596N. arXiv:1506.01354Freely accessible. doi:10.1038/srep35596. 
  39. ^ Stuart Gillespie (21 October 2016). "The universe is expanding at an accelerating rate – or is it?". University of Oxford - News & Events - Science Blog (WP:NEWSBLOG). 
  40. ^ Krauss, Lawrence M.; Scherrer, Robert J. (2007-06-28). "The return of a static universe and the end of cosmology". General Relativity and Gravitation. 39 (10): 1545–1550. Bibcode:2007GReGr..39.1545K. arXiv:0704.0221Freely accessible. doi:10.1007/s10714-007-0472-9. 
  41. ^ John Baez, "The End of the Universe", 7 February 2016.