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The accelerating expansion of the universe is the observation that the universe appears to be expanding at an increasing rate. In formal terms, this means that the cosmic scale factor $a (t)$ has a positive second derivative,^[1] so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.^[2]

The expansion of the universe has been accelerating since the universe entered its dark-energy-dominated era, at redshift $z \approx 0.4$ (roughly 5 billion years ago).^[3]^{[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, known as ΛCDM (lambda cold dark matter).

The accelerated expansion was discovered in 1998, when two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team simultaneously obtained results suggesting an acceleration in the expansion of the universe by using distant type Ia supernovae as standard candles.^[4]^[5]^[6] The discovery was unexpected, cosmologists at the time expecting a deceleration in the expansion of the universe, and amounts to the realization that the universe is currently in a "dark-energy-dominated era". 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 other new results about the clustering of galaxies.

In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.^[8]

Background

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Dark Ages

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Accelerated expansion

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(billion years ago)

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.

H^{2}={\left({\frac {\dot {a}}{a}}\right)}^{2}={\frac {8{\pi }G}{3}}\rho -{\frac {{\mathrm {K} }c^{2}}{R^{2}a^{2}}}

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

\rho _{c}={\frac {3H^{2}}{8{\pi }G}}

and the density parameter

\Omega ={\frac {\rho }{\rho _{c}}}

We can then rewrite the Hubble parameter as

H(a)=H_{0}{\sqrt {{\Omega _{k}a^{-2}+\Omega }_{m}a^{-3}+\Omega _{r}a^{-4}+\Omega _{\mathrm {DE} }a^{-3(1+w)}}}

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

{\frac {\ddot {a}}{a}}=-{\frac {4{\pi }G}{3}}\left(\rho +{\frac {3P}{c^{2}}}\right)

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 $q 0$ .^[12]^{[page needed]} Current observations point towards this deceleration parameter being negative.

Evidence for acceleration

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

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 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.

a(t)={\frac {1}{1+z}}

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. 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 $Ω M = 0.2$ 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

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

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 $Ω m$ are obtained which confirm a low matter density and a non zero amount of dark energy.^[15]

Age of the universe

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.

t_{0}=\int _{0}^{1}{\frac {da}{\dot {a}}}

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

Dark energy

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

P=wc^{2}\rho

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 ( $Ω λ > 0$ ) and a current acceleration of the expansion ( $q 0 < 0$ ).^[14]

Phantom energy

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 $H 0$ = 70 km·s⁻¹·Mpc⁻¹, the time remaining before the universe ends in this "Big Rip" is 22 billion years.^[20]

Alternative theories

Other explanations for the accelerating universe include 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]

Theories for the consequences to the universe

As the universe expands, the density of radiation and ordinary and 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.^[29]

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

Notes

^ ^[3]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: $a (t) \propto t 2/3 (1 + w)$ (for constant $w$ ). During the radiation-dominated era, $a (t) \propto t 1/2$ ; during the matter-dominated era, $a (t) \propto t 2/3$ ; and for the dark energy-dominated era, assuming $w = -1$ , asymptotically $a (t) \propto exp(Ht)$ ."
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 $z \sim$ 0.4 and age $t \sim$ 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."

References

^ Jones, Mark H.; Lambourne, Robert J. (2004). An Introduction to Galaxies and Cosmology. Cambridge University Press. p. 244. ISBN 978-0-521-83738-5.
^ "Is the universe expanding faster than the speed of light?".
^ ^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. arXiv:0803.0982. Bibcode:2008ARA&A..46..385F. doi:10.1146/annurev.astro.46.060407.145243.
^ "Nobel physics prize honours accelerating universe find". BBC News. 2011-10-04.
^ "The Nobel Prize in Physics 2011". Nobelprize.org. Retrieved 2011-10-06.
^ Peebles, P. J. E.; Ratra, Bharat (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75 (2): 559–606. arXiv:astro-ph/0207347. Bibcode:2003RvMP...75..559P. doi:10.1103/RevModPhys.75.559.
^ Weinberg, Steven (2008). Cosmology. Oxford University Press.^{[ISBN missing]}
^ Radford, Tim (2016-06-03). "Universe is expanding up to 9% faster than we thought, say scientists". The Guardian. Retrieved 2016-06-03.
^ 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.
^ Nemiroff, Robert J.; Patla, Bijunath. "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536.
^ ^a ^b Lapuente, P. (2010). "Baryon Acoustic Oscillations". Dark Energy: Observational and Theoretical Approaches. Cambridge, UK: Cambridge University Press.^{[ISBN missing]}
^ ^a ^b ^c Ryden, Barbara (2003). Introduction to Cosmology. San Francisco, CA: Addison Wesley. ISBN 978-0-8053-8912-8.
^ 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/0609591. {{cite journal}}: Cite journal requires |journal= (help)
^ ^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. arXiv:astro-ph/9805201. Bibcode:1998AJ....116.1009R. doi:10.1086/300499.
^ ^a ^b ^c Pain, Reynald; Astier, Pierre (2012). "Observational evidence of the accelerated expansion of the Universe". Comptes Rendus Physique. 13 (6): 521–538. arXiv:1204.5493. doi:10.1016/j.crhy.2012.04.009.
^ Hinshaw, G. (2014). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results". Astrophysical Journal Supplement. 180: 225–245. arXiv:0803.0732. Bibcode:2009ApJS..180..225H. doi:10.1088/0067-0049/180/2/225.
^ 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. arXiv:astro-ph/0501171. Bibcode:2005ApJ...633..560E. doi:10.1086/466512.
^ Dekel, Avishai (1999). Formation of Structure in the Universe. New York, NY: Cambridge University Press.^{[ISBN missing]}
^ 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. arXiv:astro-ph/0302506. Bibcode:2003PhRvL..91g1301C. doi:10.1103/PhysRevLett.91.071301. PMID 12935004.
^ 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. arXiv:astro-ph/9908168. Bibcode:2002PhLB..545...23C. doi:10.1016/S0370-2693(02)02589-3.
^ 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). arXiv:0711.0958. doi:10.1086/587744.
^ Benoit-Lévy, A.; Chardin, G. (2012). "Introducing the Dirac–Milne universe". Astronomy and Astrophysics. 537: A78. doi:10.1051/0004-6361/201016103.
^ 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. doi:10.1007/s10509-012-0992-y.
^ Villata, M. (2013). "On the nature of dark energy: the lattice Universe". Astrophysics and Space Science. 345: 1. arXiv:1302.3515. doi:10.1007/s10509-013-1388-3.
^ "Backreaction: directions of progress". Classical and Quantum Gravity. 28: 164008. arXiv:1102.0408. Bibcode:2011CQGra..28p4008R. doi:10.1088/0264-9381/28/16/164008.
^ "Backreaction in Late-Time Cosmology". Annual Review of Nuclear and Particle Science. 62: 57–79. arXiv:1112.5335. Bibcode:2012ARNPS..62...57B. doi:10.1146/annurev.nucl.012809.104435.
^ ^a ^b "Is dark energy an illusion?". New Scientist. 2007.
^ "A Cosmic 'Tardis': What the Universe Has In Common with 'Doctor Who'". Space.com.
^ 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. arXiv:0704.0221. Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9.

[4] [3]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: $a (t) \propto t 2/3 (1 + w)$ (for constant $w$ ). During the radiation-dominated era, $a (t) \propto t 1/2$ ; during the matter-dominated era, $a (t) \propto t 2/3$ ; and for the dark energy-dominated era, assuming $w = -1$ , asymptotically $a (t) \propto exp(Ht)$ ."
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 $z \sim$ 0.4 and age $t \sim$ 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] Jones, Mark H.; Lambourne, Robert J. (2004). An Introduction to Galaxies and Cosmology. Cambridge University Press. p. 244. ISBN 978-0-521-83738-5.

[2] "Is the universe expanding faster than the speed of light?".

[Frieman-3] 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. arXiv:0803.0982. Bibcode:2008ARA&A..46..385F. doi:10.1146/annurev.astro.46.060407.145243.

[BBC-5] "Nobel physics prize honours accelerating universe find". BBC News. 2011-10-04.

[6] "The Nobel Prize in Physics 2011". Nobelprize.org. Retrieved 2011-10-06.

[peebles-7] Peebles, P. J. E.; Ratra, Bharat (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75 (2): 559–606. arXiv:astro-ph/0207347. Bibcode:2003RvMP...75..559P. doi:10.1103/RevModPhys.75.559.

[8] Weinberg, Steven (2008). Cosmology. Oxford University Press.^{[ISBN missing]}

[TG-20160603-9] Radford, Tim (2016-06-03). "Universe is expanding up to 9% faster than we thought, say scientists". The Guardian. Retrieved 2016-06-03.

[Penzias&Wilson-10] 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.

[11] Nemiroff, Robert J.; Patla, Bijunath. "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536.

[Bassett-12] Lapuente, P. (2010). "Baryon Acoustic Oscillations". Dark Energy: Observational and Theoretical Approaches. Cambridge, UK: Cambridge University Press.^{[ISBN missing]}

[Ryden-13] Ryden, Barbara (2003). Introduction to Cosmology. San Francisco, CA: Addison Wesley. ISBN 978-0-8053-8912-8.

[14] 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/0609591. {{cite journal}}: Cite journal requires |journal= (help)

[Riess-15] 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. arXiv:astro-ph/9805201. Bibcode:1998AJ....116.1009R. doi:10.1086/300499.

[Pain-16] Pain, Reynald; Astier, Pierre (2012). "Observational evidence of the accelerated expansion of the Universe". Comptes Rendus Physique. 13 (6): 521–538. arXiv:1204.5493. doi:10.1016/j.crhy.2012.04.009.

[17] Hinshaw, G. (2014). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results". Astrophysical Journal Supplement. 180: 225–245. arXiv:0803.0732. Bibcode:2009ApJS..180..225H. doi:10.1088/0067-0049/180/2/225.

[18] 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. arXiv:astro-ph/0501171. Bibcode:2005ApJ...633..560E. doi:10.1086/466512.

[19] Dekel, Avishai (1999). Formation of Structure in the Universe. New York, NY: Cambridge University Press.^{[ISBN missing]}

[20] 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. arXiv:astro-ph/0302506. Bibcode:2003PhRvL..91g1301C. doi:10.1103/PhysRevLett.91.071301. PMID 12935004.

[21] 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. arXiv:astro-ph/9908168. Bibcode:2002PhLB..545...23C. doi:10.1016/S0370-2693(02)02589-3.

[22] 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). arXiv:0711.0958. doi:10.1086/587744.

[benoit-levy-23] Benoit-Lévy, A.; Chardin, G. (2012). "Introducing the Dirac–Milne universe". Astronomy and Astrophysics. 537: A78. doi:10.1051/0004-6361/201016103.

[Hajdukovic-24] 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. doi:10.1007/s10509-012-0992-y.

[villata13-25] Villata, M. (2013). "On the nature of dark energy: the lattice Universe". Astrophysics and Space Science. 345: 1. arXiv:1302.3515. doi:10.1007/s10509-013-1388-3.

[26] "Backreaction: directions of progress". Classical and Quantum Gravity. 28: 164008. arXiv:1102.0408. Bibcode:2011CQGra..28p4008R. doi:10.1088/0264-9381/28/16/164008.

[27] "Backreaction in Late-Time Cosmology". Annual Review of Nuclear and Particle Science. 62: 57–79. arXiv:1112.5335. Bibcode:2012ARNPS..62...57B. doi:10.1146/annurev.nucl.012809.104435.

[NS2007-28] "Is dark energy an illusion?". New Scientist. 2007.

[29] "A Cosmic 'Tardis': What the Universe Has In Common with 'Doctor Who'". Space.com.

[30] 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. arXiv:0704.0221. Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9.

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@@ Line 1: / Line 1: @@
 {{context|date=April 2016}}
 {{cosmology}}
-The '''accelerating expansion of the universe''' is the observation that the [[universe]] appears to be [[Metric expansion of space|expanding]] at an increasing rate.  In formal terms, this means that the [[Scale factor (cosmology)|cosmic scale factor]] <math>a(t)</math> has a positive [[second derivative]],<ref>{{cite book | last = Jones | first = Mark H. |author2= Robert J. Lambourne | title = An Introduction to Galaxies and Cosmology | publisher =Cambridge University Press | date=  2004 | page = [https://books.google.com/books?id=36K1PfetZegC&lpg=PP1&pg=PA244#v=onepage&q&f=false 244] | isbn = 978-0-521-83738-5 }}</ref> so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.<ref>[http://curious.astro.cornell.edu/the-universe/cosmology-and-the-big-bang/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate Is the universe expanding faster than the speed of light?] (see final paragraph)</ref>
+The '''accelerating expansion of the universe''' is the observation that the [[universe]] appears to be [[Metric expansion of space|expanding]] at an increasing rate.  In formal terms, this means that the [[Scale factor (cosmology)|cosmic scale factor]] {{math|''a''(''t'')}} has a positive [[second derivative]],<ref>{{cite book | last = Jones | first = Mark H. |first2= Robert J. |last2 = Lambourne | title = An Introduction to Galaxies and Cosmology | publisher =Cambridge University Press | date=  2004 | page = [https://books.google.com/books?id=36K1PfetZegC&lpg=PP1&pg=PA244#v=onepage&q&f=false 244] | isbn = 978-0-521-83738-5 }}</ref> so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.<ref>{{cite web|url=http://curious.astro.cornell.edu/the-universe/cosmology-and-the-big-bang/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate|title=Is the universe expanding faster than the speed of light?}}</ref>
-The expansion of the universe has been accelerating since the universe entered its [[dark-energy-dominated era]], at [[redshift]] z≈0.4 (roughly 5 billion years ago).<ref name="Frieman">{{Cite journal|last=Frieman|first=Joshua A.|last2=Turner|first2=Michael S.|last3=Huterer|first3=Dragan|date=2008-01-01|title=Dark Energy and the Accelerating Universe|url=http://dx.doi.org/10.1146/annurev.astro.46.060407.145243|journal=Annual Review of Astronomy and Astrophysics|volume=46|issue=1|pages=385–432|arxiv=0803.0982|bibcode=2008ARA&A..46..385F|doi=10.1146/annurev.astro.46.060407.145243}}</ref> {{refn|1= <ref name="Frieman" /> 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)."<br />
+The expansion of the universe has been accelerating since the universe entered its [[dark-energy-dominated era]], at [[redshift]] {{math|''z'' ≈ 0.4}} (roughly 5&nbsp;billion years ago).<ref name="Frieman">{{Cite journal|last=Frieman|first=Joshua A.|last2=Turner|first2=Michael S.|last3=Huterer|first3=Dragan|date=2008-01-01|title=Dark Energy and the Accelerating Universe|url=http://dx.doi.org/10.1146/annurev.astro.46.060407.145243|journal=Annual Review of Astronomy and Astrophysics|volume=46|issue=1|pages=385–432|arxiv=0803.0982|bibcode=2008ARA&A..46..385F|doi=10.1146/annurev.astro.46.060407.145243}}</ref>{{refn|1= <ref name="Frieman" />Frieman, Turner & Huterer (2008) p. 6: "The Universe has gone through three distinct eras: radiation-dominated, {{math|''z'' ≳ 3000}}; matter-dominated, {{math|3000 ≳ ''z'' ≳ 0.5}}; and dark-energy-dominated, {{math|''z'' ≲ 0.5}}. The evolution of the scale factor is controlled by the dominant energy form: {{math|''a''(''t'') ∝ ''t''<sup>2/3</sup>(1 + ''w'')}} (for constant {{mvar|w}}). During the radiation-dominated era, {{math|''a''(''t'') ∝ ''t''<sup>1/2</sup>}}; during the matter-dominated era, {{math|''a''(''t'') ∝ ''t''<sup>2/3</sup>}}; and for the dark energy-dominated era, assuming {{math|''w'' {{=}} −1}}, asymptotically {{math|''a''(''t'') ∝ exp(''Ht'')}}."<br />
-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."|group="notes"}}
+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&nbsp;±&nbsp;0.02, and the equation-of-state parameter, {{mvar|w}}&nbsp;≈ −1&nbsp;±&nbsp;0.1 (stat) ±&nbsp;0.1 (sys), assuming that {{mvar|w}} is constant. This implies that the Universe began accelerating at redshift {{math|''z'' ∼}}&nbsp;0.4 and age {{math|''t'' ∼}}&nbsp;10&nbsp;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."|group="notes"}}
-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 [[physical cosmology|cosmology]], known as [[Lambda-CDM model|ΛCDM]] ("Lambda cold dark matter").
+Within the framework of [[general relativity]], an accelerating expansion can be accounted for by a positive value of the [[cosmological constant]] {{mvar|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 {{mvar|Λ}}) is used in the current standard model of [[physical cosmology|cosmology]], known as [[Lambda-CDM model|ΛCDM]] (lambda cold dark matter).
-The accelerated expansion was discovered in 1998, when  two independent projects, the [[Supernova Cosmology Project]] and the [[High-Z Supernova Search Team]] simultaneously obtained results suggesting an acceleration in the expansion of the universe by using distant [[type Ia supernovae]] as [[Cosmic distance ladder#Standard candles|standard candles]].<ref name="BBC">{{cite news|url=http://www.bbc.co.uk/news/science-environment-15165371|title=Nobel physics prize honours accelerating universe find|publisher=BBC News|date=October 4, 2011}}</ref><ref>{{cite web|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/# |title=The Nobel Prize in Physics 2011 |publisher=Nobelprize.org |accessdate=2011-10-06}}</ref><ref name="peebles">{{cite journal|author=Peebles, P. J. E.|author2=Ratra, Bharat|last-author-amp=yes |title=The cosmological constant and dark energy|date=2003|journal=Reviews of Modern Physics|arxiv=astro-ph/0207347|volume=75|issue=2|pages=559–606|doi = 10.1103/RevModPhys.75.559|bibcode=2003RvMP...75..559P}}</ref> The discovery was unexpected, cosmologists at the time expecting a deceleration in the expansion of the universe, and amounts to the realization that the universe is currently in a "dark-energy-dominated era". Three members of these two groups have subsequently been awarded [[Nobel Prize]]s for their discovery.<ref>''Cosmology'', Steven Weinberg, Oxford University Press, 2008</ref> Confirmatory evidence has been found in [[baryon acoustic oscillations]] and other new results about the clustering of galaxies.
+The accelerated expansion was discovered in 1998, when two independent projects, the [[Supernova Cosmology Project]] and the [[High-Z Supernova Search Team]] simultaneously obtained results suggesting an acceleration in the expansion of the universe by using distant [[type Ia supernovae]] as [[Cosmic distance ladder#Standard candles|standard candles]].<ref name="BBC">{{cite news|url=http://www.bbc.co.uk/news/science-environment-15165371|title=Nobel physics prize honours accelerating universe find|publisher=BBC News|date=2011-10-04}}</ref><ref>{{cite web|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/# |title=The Nobel Prize in Physics 2011 |publisher=Nobelprize.org |accessdate=2011-10-06}}</ref><ref name="peebles">{{cite journal|author=Peebles|first1=P. J. E.|author2=Ratra|first2=Bharat|title=The cosmological constant and dark energy|date=2003|journal=Reviews of Modern Physics|arxiv=astro-ph/0207347|volume=75|issue=2|pages=559–606|doi = 10.1103/RevModPhys.75.559|bibcode=2003RvMP...75..559P}}</ref> The discovery was unexpected, cosmologists at the time expecting a deceleration in the expansion of the universe, and amounts to the realization that the universe is currently in a "dark-energy-dominated era". Three members of these two groups have subsequently been awarded [[Nobel Prize]]s for their discovery.<ref>{{cite book|title=Cosmology|first=Steven|last=Weinberg|publisher=Oxford University Press|date=2008|isbn=}}{{ISBN missing}}</ref> Confirmatory evidence has been found in [[baryon acoustic oscillations]] and other new results about the clustering of galaxies.
-In June 2016, [[NASA]] and [[ESA]] scientists reported that the [[universe]] was found to be expanding 5% to 9% faster than thought earlier, based on studies using the [[Hubble Space Telescope]].<ref name="TG-20160603">{{cite news |last=Radford |first=Tim |title=Universe is expanding up to 9% faster than we thought, say scientists |url=https://www.theguardian.com/science/2016/jun/03/universe-is-expanding-up-to-9-faster-than-we-thought-say-scientists |date=3 June 2016 |work=[[The Guardian]] |accessdate=3 June 2016 }}</ref>
+In June 2016, [[NASA]] and [[ESA]] scientists reported that the [[universe]] was found to be expanding 5% to 9% faster than thought earlier, based on studies using the [[Hubble Space Telescope]].<ref name="TG-20160603">{{cite news |last=Radford |first=Tim |title=Universe is expanding up to 9% faster than we thought, say scientists |url=https://www.theguardian.com/science/2016/jun/03/universe-is-expanding-up-to-9-faster-than-we-thought-say-scientists |date=2016-06-03 |work=[[The Guardian]] |accessdate=2016-06-03 }}</ref>
 ==Background==
 {{Nature timeline}}
 {{further information|Cosmological constant|Lambda-CDM model|Hubble's law|Friedmann–Lemaître–Robertson–Walker metric|Friedman equations}}
-In the decades since the detection of [[cosmic microwave background]] (CMB) in 1965,<ref name="Penzias&Wilson">{{cite journal |last=Penzias |first=A. A. |last2=Wilson|first2=R. W. |date=1965 |title=A Measurement of Excess Antenna Temperature at 4080 Mc/s |journal=[[The Astrophysical Journal]] |volume=142 |issue=1 |pages=419–421 |bibcode=1965ApJ...142..419P |doi=10.1086/148307}}</ref> the [[Big Bang]] model has become the most accepted model explaining the evolution of our universe. The [[Friedmann equations|Friedmann equation]] defines how the [[energy]] in the universe drives its expansion.
+In the decades since the detection of [[cosmic microwave background]] (CMB) in 1965,<ref name="Penzias&Wilson">{{cite journal |last=Penzias |first=A. A. |last2=Wilson|first2=R. W. |date=1965 |title=A Measurement of Excess Antenna Temperature at 4080&nbsp;Mc/s |journal=[[The Astrophysical Journal]] |volume=142 |issue=1 |pages=419–421 |bibcode=1965ApJ...142..419P |doi=10.1086/148307}}</ref> the [[Big Bang]] model has become the most accepted model explaining the evolution of our universe. The [[Friedmann equations|Friedmann equation]] defines how the [[energy]] in the universe drives its expansion.
 :<math> H^2={\left ( \frac{\dot{a}}{a} \right )}^2=\frac{8{\pi}G}{3}\rho-\frac{{\Kappa}c^2}{R^2a^2} </math>
-where <math>\Kappa</math> represents the [[curvature of the universe]], <math>a(t)</math> is the [[Scale factor (cosmology)|scale factor]], <math>\rho</math> is the total energy density of the universe, and <math>H</math> is the [[Hubble parameter]].<ref>{{cite journal|last1=Nemiroff|first1=Robert J.|last2=Patla|first2=Bijunath|title=Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations|journal=American Journal of Physics|volume=76|issue=3|pages=265|doi=10.1119/1.2830536|arxiv = astro-ph/0703739 |bibcode = 2008AmJPh..76..265N }}</ref>
+where {{mvar|Κ}} represents the [[curvature of the universe]], {{math|''a''(''t'')}} is the [[Scale factor (cosmology)|scale factor]], {{mvar|ρ}} is the total energy density of the universe, and {{mvar|H}} is the [[Hubble parameter]].<ref>{{cite journal|last1=Nemiroff|first1=Robert J.|last2=Patla|first2=Bijunath|title=Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations|journal=American Journal of Physics|volume=76|issue=3|pages=265|doi=10.1119/1.2830536|arxiv = astro-ph/0703739 |bibcode = 2008AmJPh..76..265N }}</ref>
 We define a [[Critical density (cosmology)|critical density]]
@@ Line 26: / Line 26: @@
 We can then rewrite the Hubble parameter as
-:<math> H(a) = H_0 \sqrt{{\Omega_ka^{-2} + \Omega}_ma^{-3} + \Omega_ra^{-4} + \Omega_{DE}a^{-3(1+w)}} </math>
+:<math> H(a) = H_0 \sqrt{{\Omega_ka^{-2} + \Omega}_ma^{-3} + \Omega_ra^{-4} + \Omega_\mathrm{DE}a^{-3(1+w)}} </math>
-where the four currently hypothesized contributors to the energy density of the universe are [[Shape of the universe|curvature]], [[matter]], [[radiation]] and [[dark energy]].<ref name=Bassett>Lapuente, P.. "Baryon Acoustic Oscillations." Dark energy: observational and theoretical approaches. Cambridge, UK: Cambridge University Press, 2010.</ref> 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.
+where the four currently hypothesized contributors to the energy density of the universe are [[Shape of the universe|curvature]], [[matter]], [[radiation]] and [[dark energy]].<ref name=Bassett>{{cite book|last=Lapuente|first=P.|chapter=Baryon Acoustic Oscillations|title=Dark Energy: Observational and Theoretical Approaches|location=Cambridge, UK|publisher=Cambridge University Press|date=2010|isbn=}}{{ISBN missing}}</ref> 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 [[Friedmann equations|acceleration equation]] describes the evolution of the scale factor with time
@@ Line 34: / Line 34: @@
 :<math> \frac{\ddot{a}}{a}=-\frac{4{\pi}G}{3}\left( \rho + \frac{3P}{c^2} \right) </math>
-where the [[pressure]] P is defined by the cosmological model chosen. (see [[Accelerating universe#Explanatory models|explanatory models]] below)
+where the [[pressure]] {{mvar|P}} is defined by the cosmological model chosen. (see [[Accelerating universe#Explanatory models|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]] <math>q_0</math>.<ref name=Ryden>Ryden, Barbara. "Introduction to Cosmology." Physics Today: 77. Print.</ref> Current observations point towards this deceleration parameter being negative.
+Physicists at one time were so assured of the deceleration of the universe's expansion that they introduced a so-called [[deceleration parameter]] {{math|''q''<sub>0</sub>}}.<ref name=Ryden>{{cite book|title=Introduction to Cosmology|last=Ryden|first=Barbara|location=San Francisco, CA|publisher=Addison Wesley|date=2003|ISBN=978-0-8053-8912-8}}</ref>{{Page needed|date=September 2016}} Current observations point towards this deceleration parameter being negative.
 ==Evidence for acceleration==
@@ Line 43: / Line 43: @@
 ===Supernova observation===
 [[File:Asymmetric Ashes (artist's impression).jpg|thumb|left|200px|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 supernova]]e, which are exploding [[white dwarf]]s that have exceeded their [[Chandrasekhar limit|stability limit]]. Because they all have similar masses, their intrinsic [[luminosity]] is standardizable. Repeated imaging of selected areas of 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).<ref>Albrecht, A., Bernstein, G., Cahn, R., et al. Report of the Dark Energy TaskForce. ArXiv Astrophysics e-prints, September 2006.</ref> [[Spectral line]]s of their light can be used to determine their [[redshift]].
+The first evidence for acceleration came from the observation of [[Type Ia supernova]]e, which are exploding [[white dwarf]]s that have exceeded their [[Chandrasekhar limit|stability limit]]. Because they all have similar masses, their intrinsic [[luminosity]] is standardizable. Repeated imaging of selected areas of 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).<ref>{{cite journal|first1=Andreas|last1=Albrecht|first2=Gary|last2=Bernstein|first3=Robert|last3=Cahn|first4=Wendy L.|last4=Freedman|first5=Jacqueline|last5=Hewitt|first6=Wayne|last6=Hu|first7=John|last7=Huth|first8=Marc|last8=Kamionkowski|first9=Edward W.|last9=Kolb|first10=Lloyd|last10=Knox|first11=John C.|last11=Mather|first12=Suzanne|last12=Staggs|first13=Nicholas B.|last13=Suntzeff|title=Report of the Dark Energy Task Force|date=2006-09-20|arxiv=astro-ph/0609591}}</ref> [[Spectral line]]s 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.
+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 {{mvar|z}} directly gives the [[cosmic scale factor]] at the time the supernova exploded.
 :<math> a(t) = \frac{1}{1+z} </math>
-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 2/3 to 1.0 times 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. 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 <math> \Omega_M = 0.2 </math> universe without a cosmological constant".<ref name=Riess>{{cite journal|last1=Riess|first1=Adam G.|last2=Filippenko|first2=Alexei V.|last3=Challis|first3=Peter|last4=Clocchiatti|first4=Alejandro|last5=Diercks|first5=Alan|last6=Garnavich|first6=Peter M.|last7=Gilliland|first7=Ron L.|last8=Hogan|first8=Craig J.|last9=Jha|first9=Saurabh|last10=Kirshner|first10=Robert P.|last11=Leibundgut|first11=B.|last12=Phillips|first12=M. M.|last13=Reiss|first13=David|last14=Schmidt|first14=Brian P.|last15=Schommer|first15=Robert A.|last16=Smith|first16=R. Chris|last17=Spyromilio|first17=J.|last18=Stubbs|first18=Christopher|last19=Suntzeff|first19=Nicholas B.|last20=Tonry|first20=John|title=Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant|journal=The Astronomical Journal|volume=116|issue=3|pages=1009–1038|doi=10.1086/300499|bibcode=1998AJ....116.1009R|arxiv = astro-ph/9805201 }}</ref> This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.<ref name = Pain>Pain, Reynald. "Observational evidence of the accelerated expansion of the Universe." Comptes Rendus Physique: 521-538. [http://arxiv.org/abs/1204.5493]</ref>
+So a supernova with a measured redshift {{math|''z'' {{=}} 0.5}} implies the universe was {{sfrac|1|1 + 0.5}}&nbsp;=&nbsp;{{sfrac|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. 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 {{math|''Ω''<sub>M</sub> {{=}} 0.2}} universe without a cosmological constant".<ref name=Riess>{{cite journal|last1=Riess|first1=Adam G.|last2=Filippenko|first2=Alexei V.|last3=Challis|first3=Peter|last4=Clocchiatti|first4=Alejandro|last5=Diercks|first5=Alan|last6=Garnavich|first6=Peter M.|last7=Gilliland|first7=Ron L.|last8=Hogan|first8=Craig J.|last9=Jha|first9=Saurabh|last10=Kirshner|first10=Robert P.|last11=Leibundgut|first11=B.|last12=Phillips|first12=M. M.|last13=Reiss|first13=David|last14=Schmidt|first14=Brian P.|last15=Schommer|first15=Robert A.|last16=Smith|first16=R. Chris|last17=Spyromilio|first17=J.|last18=Stubbs|first18=Christopher|last19=Suntzeff|first19=Nicholas B.|last20=Tonry|first20=John|title=Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant|journal=The Astronomical Journal|volume=116|issue=3|pages=1009–1038|doi=10.1086/300499|bibcode=1998AJ....116.1009R|arxiv = astro-ph/9805201 }}</ref> This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.<ref name = Pain>{{cite journal|last=Pain|first=Reynald|last2=Astier|first2=Pierre|title=Observational evidence of the accelerated expansion of the Universe|journal=Comptes Rendus Physique|volume=13|issue=6|pages=521–538|arxiv=1204.5493|doi=10.1016/j.crhy.2012.04.009|date=2012}}</ref>
 ===Baryon acoustic oscillations===
 {{main article|Baryon acoustic oscillations}}
-In the early universe before [[recombination (cosmology)|recombination]] and [[decoupling (cosmology)|decoupling]] took place, [[photon]]s and matter existed in a [[Structure formation#Primordial plasma|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.<ref name=Ryden/> 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,<ref>{{cite journal | last1 = Hinshaw | first1 = G. | date = 2014 | title = Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results | doi =10.1088/0067-0049/180/2/225 | journal = Astrophysical Journal Supplement | volume = 180 | pages = 225–245 |arxiv = 0803.0732 |bibcode = 2009ApJS..180..225H }}</ref> photons separated from matter and were able to [[free streaming|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.
+In the early universe before [[recombination (cosmology)|recombination]] and [[decoupling (cosmology)|decoupling]] took place, [[photon]]s and matter existed in a [[Structure formation#Primordial plasma|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.<ref name=Ryden/>{{Page needed|date=September 2016}} 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,<ref>{{cite journal | last1 = Hinshaw | first1 = G. | date = 2014 | title = Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results | doi =10.1088/0067-0049/180/2/225 | journal = Astrophysical Journal Supplement | volume = 180 | pages = 225–245 |arxiv = 0803.0732 |bibcode = 2009ApJS..180..225H }}</ref> photons separated from matter and were able to [[free streaming|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 <math>100h^{-1}</math> [[Parsec#Megaparsecs and Gigaparsecs|Mpc]],<ref name=Bassett/> 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.<ref>{{cite journal|last1=Eisenstein|first1=Daniel J.|last2=Zehavi|first2=Idit|last3=Hogg|first3=David W.|last4=Scoccimarro|first4=Roman|last5=Blanton|first5=Michael R.|last6=Nichol|first6=Robert C.|last7=Scranton|first7=Ryan|last8=Seo|first8=Hee‐Jong|last9=Tegmark|first9=Max|last10=Zheng|first10=Zheng|last11=Anderson|first11=Scott F.|last12=Annis|first12=Jim|last13=Bahcall|first13=Neta|last14=Brinkmann|first14=Jon|last15=Burles|first15=Scott|last16=Castander|first16=Francisco J.|last17=Connolly|first17=Andrew|last18=Csabai|first18=Istvan|last19=Doi|first19=Mamoru|last20=Fukugita|first20=Masataka|last21=Frieman|first21=Joshua A.|last22=Glazebrook|first22=Karl|last23=Gunn|first23=James E.|last24=Hendry|first24=John S.|last25=Hennessy|first25=Gregory|last26=Ivezić|first26=Zeljko|last27=Kent|first27=Stephen|last28=Knapp|first28=Gillian R.|last29=Lin|first29=Huan|last30=Loh|first30=Yeong‐Shang|last31=Lupton|first31=Robert H.|last32=Margon|first32=Bruce|last33=McKay|first33=Timothy A.|last34=Meiksin|first34=Avery|last35=Munn|first35=Jeffery A.|last36=Pope|first36=Adrian|last37=Richmond|first37=Michael W.|last38=Schlegel|first38=David|last39=Schneider|first39=Donald P.|last40=Shimasaku|first40=Kazuhiro|last41=Stoughton|first41=Christopher|last42=Strauss|first42=Michael A.|last43=SubbaRao|first43=Mark|last44=Szalay|first44=Alexander S.|last45=Szapudi|first45=Istvan|last46=Tucker|first46=Douglas L.|last47=Yanny|first47=Brian|last48=York|first48=Donald G.|title=Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies|journal=The Astrophysical Journal|date=10 November 2005|volume=633|issue=2|pages=560–574|doi=10.1086/466512|bibcode=2005ApJ...633..560E|arxiv = astro-ph/0501171 }}</ref>
+Peaks have been found in the correlation function (the probability that two galaxies will be a certain distance apart) at {{nowrap|100 ''h''<sup>−1</sup> [[Parsec#Megaparsecs and Gigaparsecs|Mpc]]}},<ref name=Bassett/> 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.<ref>{{cite journal|last1=Eisenstein|first1=Daniel J.|last2=Zehavi|first2=Idit|last3=Hogg|first3=David W.|last4=Scoccimarro|first4=Roman|last5=Blanton|first5=Michael R.|last6=Nichol|first6=Robert C.|last7=Scranton|first7=Ryan|last8=Seo|first8=Hee‐Jong|last9=Tegmark|first9=Max|last10=Zheng|first10=Zheng|last11=Anderson|first11=Scott F.|last12=Annis|first12=Jim|last13=Bahcall|first13=Neta|last14=Brinkmann|first14=Jon|last15=Burles|first15=Scott|last16=Castander|first16=Francisco J.|last17=Connolly|first17=Andrew|last18=Csabai|first18=Istvan|last19=Doi|first19=Mamoru|last20=Fukugita|first20=Masataka|last21=Frieman|first21=Joshua A.|last22=Glazebrook|first22=Karl|last23=Gunn|first23=James E.|last24=Hendry|first24=John S.|last25=Hennessy|first25=Gregory|last26=Ivezić|first26=Zeljko|last27=Kent|first27=Stephen|last28=Knapp|first28=Gillian R.|last29=Lin|first29=Huan|last30=Loh|first30=Yeong‐Shang|last31=Lupton|first31=Robert H.|last32=Margon|first32=Bruce|last33=McKay|first33=Timothy A.|last34=Meiksin|first34=Avery|last35=Munn|first35=Jeffery A.|last36=Pope|first36=Adrian|last37=Richmond|first37=Michael W.|last38=Schlegel|first38=David|last39=Schneider|first39=Donald P.|last40=Shimasaku|first40=Kazuhiro|last41=Stoughton|first41=Christopher|last42=Strauss|first42=Michael A.|last43=SubbaRao|first43=Mark|last44=Szalay|first44=Alexander S.|last45=Szapudi|first45=Istvan|last46=Tucker|first46=Douglas L.|last47=Yanny|first47=Brian|last48=York|first48=Donald G.|title=Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies|journal=The Astrophysical Journal|date=2005-11-10|volume=633|issue=2|pages=560–574|doi=10.1086/466512|bibcode=2005ApJ...633..560E|arxiv = astro-ph/0501171 }}</ref>
 ===Clusters of galaxies===
-Measuring the mass functions of [[galaxy cluster]]s, which describe the [[number density]] of the clusters above a threshold mass, also provides evidence for dark energy.<ref>Dekel, Avishai. Formation of structure in the Universe. New York: Cambridge University Press, 1999.</ref> By comparing these mass functions at high and low redshifts to those predicted by different cosmological models, values for <math> w </math> and <math> \Omega_m </math> are obtained which confirm a low matter density and a non zero amount of dark energy.<ref name = Pain/>
+Measuring the mass functions of [[galaxy cluster]]s, which describe the [[number density]] of the clusters above a threshold mass, also provides evidence for dark energy.<ref>{{cite book|last=Dekel|first=Avishai|title=Formation of Structure in the Universe|location=New York, NY|publisher=Cambridge University Press|date=1999|isbn=}}{{ISBN missing}}</ref> By comparing these mass functions at high and low redshifts to those predicted by different cosmological models, values for {{mvar|w}} and {{mvar|Ω<sub>m</sub>}} are obtained which confirm a low matter density and a non zero amount of dark energy.<ref name = Pain/>
 ===Age of the universe===
@@ Line 64: / Line 64: @@
 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.
-:<math> t_0 = \int\limits_{0}^{1}\frac{da}{\dot{a}} </math>
+:<math> t_0 = \int_{0}^{1}\frac{da}{\dot{a}} </math>
 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.<ref name = Pain/>
@@ Line 77: / Line 77: @@
 :<math> P = wc^2\rho </math>
-where c is the speed of light, <math>\rho</math> 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 <math>\ddot{a}</math> in the [[Accelerating universe#Background|acceleration equation]] above).
+where {{mvar|c}} is the speed of light and {{mvar|ρ}} is the energy density. Different theories of dark energy suggest different values of {{mvar|w}}, with {{math|''w'' < −{{sfrac|1|3}}}} for cosmic acceleration (this leads to a positive value of {{mvar|ä}} in the [[Accelerating universe#Background|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 (<math>\Omega_\lambda</math> > 0) and a current acceleration of the expansion (<math>q_0</math> < 0).<ref name=Riess/>
+The simplest explanation for dark energy is that it is a cosmological constant or [[vacuum energy]]; in this case {{math|''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 ({{math|''Ω<sub>λ</sub>'' > 0}}) and a current acceleration of the expansion ({{math|''q''<sub>0</sub> < 0}}).<ref name=Riess/>
 ===Phantom energy===
 {{main article| Phantom energy}}
+Current observations allow the possibility of a cosmological model containing a dark energy component with equation of state {{math|''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]].<ref>{{cite journal|last1=Caldwell|first1=Robert|last2=Kamionkowski|first2=Marc|last3=Weinberg|first3=Nevin|title=Phantom Energy: Dark Energy with {{math|''w'' < −1}} Causes a Cosmic Doomsday|journal=Physical Review Letters|volume=91|issue=7|doi=10.1103/PhysRevLett.91.071301|bibcode=2003PhRvL..91g1301C|pmid=12935004|date=August 2003|pages=071301|arxiv = astro-ph/0302506 }}</ref> For example, for {{math|''w'' {{=}} −{{sfrac|3|2}}}} and {{math|''H''<sub>0</sub>}}&nbsp;= 70&nbsp;km·s<sup>−1</sup>·Mpc<sup>−1</sup>, the time remaining before the universe ends in this "Big Rip" is 22&nbsp;billion years.<ref>{{cite journal|last1=Caldwell|first1=R. R.|title=A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state|journal=Physics Letters B|volume=545|issue=1–2|date=2002|pages=23–29|doi=10.1016/S0370-2693(02)02589-3|arxiv = astro-ph/9908168 |bibcode = 2002PhLB..545...23C }}</ref>
-Current observations allow the possibility of a cosmological model containing a dark energy component with equation of state:
-:<math> w<-1 </math>
-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]].<ref>{{cite journal|last1=Caldwell|first1=Robert|last2=Kamionkowski|first2=Marc|last3=Weinberg|first3=Nevin|title=Phantom Energy: Dark Energy with w-1 Causes a Cosmic Doomsday|journal=Physical Review Letters|volume=91|issue=7|doi=10.1103/PhysRevLett.91.071301|bibcode=2003PhRvL..91g1301C|pmid=12935004|date=August 2003|pages=071301|arxiv = astro-ph/0302506 }}</ref> For example, for w = -3/2 and <math>H_0</math> = 70&nbsp;km·s<sup>−1</sup>·Mpc<sup>−1</sup>, the time remaining before the universe ends in this "Big Rip" is 22 billion years.<ref>{{cite journal|last1=Caldwell|first1=R.R|title=A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state|journal=Physics Letters B|volume=545|issue=1-2|pages=23–29|doi=10.1016/S0370-2693(02)02589-3|arxiv = astro-ph/9908168 |bibcode = 2002PhLB..545...23C }}</ref>
 ===Alternative theories===
-Other explanations for the accelerating universe include [[quintessence (physics)|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.<ref>Anaelle Halle, HongSheng Zhao, Baojiu Li (2008) "Perturbations in a non-uniform dark energy fluid: equations reveal effects of modified gravity and dark matter [http://arxiv.org/abs/0711.0958]"</ref>
+Other explanations for the accelerating universe include [[quintessence (physics)|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.<ref>{{cite journal|first1=Anaelle|last1=Halle|first2=Hongsheng|last2=Zhao|first3=Baojiu|last3=Li|date=2008|title==Perturbations in a non-uniform dark energy fluid: equations reveal effects of modified gravity and dark matter|arxiv=0711.0958|doi=10.1086/587744|journal=Astrophysical Journal Supplement Series|volume=177|issue=1}}</ref> Alternatively, some authors have argued that the universe expansion acceleration could be due to a repulsive [[gravitational interaction of antimatter]].<ref name="benoit-levy">{{cite journal|first1=A.|last1=Benoit-Lévy|first2=G.|last2=Chardin|url=http://www.aanda.org/articles/aa/full_html/2012/01/aa16103-10/aa16103-10.html|title=Introducing the Dirac–Milne universe|journal=Astronomy and Astrophysics|volume=537|page=A78|date=2012|doi=10.1051/0004-6361/201016103}}{{open access}}</ref><ref name = "Hajdukovic">{{cite journal|first=D. S.|last=Hajduković|doi=10.1007/s10509-012-0992-y|title=Quantum vacuum and virtual gravitational dipoles: the solution to the dark energy problem?|journal=Astrophysics and Space Science|volume=339|issue=1|page=1–5|date=2012}}</ref><ref name="villata13">{{cite journal|first=M.|last=Villata|doi=10.1007/s10509-013-1388-3|title=On the nature of dark energy: the lattice Universe|date=2013|journal=Astrophysics and Space Science|volume=345|page=1|arxiv=1302.3515}}</ref>
-Alternatively, some authors have argued that the universe expansion acceleration could be due to a repulsive [[gravitational interaction of antimatter]].<ref name="benoit-levy">A. Benoit-Lévy and G. Chardin, [http://www.aanda.org/articles/aa/full_html/2012/01/aa16103-10/aa16103-10.html Introducing the Dirac-Milne universe], Astronomy and Astrophysics 537, A78 (2012)</ref><ref name = "Hajdukovic">D.S. Hajdukovic, [http://link.springer.com/article/10.1007%2Fs10509-012-0992-y Quantum vacuum and virtual gravitational dipoles: the solution to the dark energy problem?], Astrophysics and Space Science 339(1), 1--5 (2012)</ref><ref name="villata13">M. Villata, [http://rd.springer.com/article/10.1007%2Fs10509-013-1388-3 On the nature of dark energy: the lattice Universe], 2013, Astrophysics and Space Science 345, 1. Also available [http://arxiv.org/pdf/1302.3515 here]</ref>
-Another type of model, the backreaction conjecture,<ref>{{cite journal | doi = 10.1088/0264-9381/28/16/164008 | volume=28 | title=Backreaction: directions of progress | journal=Classical and Quantum Gravity | pages=164008|arxiv = 1102.0408 |bibcode = 2011CQGra..28p4008R }}</ref><ref>{{cite journal | doi = 10.1146/annurev.nucl.012809.104435 | volume=62 | title=Backreaction in Late-Time Cosmology | journal=Annual Review of Nuclear and Particle Science | pages=57–79|arxiv = 1112.5335 |bibcode = 2012ARNPS..62...57B }}</ref> was proposed by cosmologist Syksy Räsänen:<ref name="NS2007">https://www.newscientist.com/article/dn11498-is-dark-energy-an-illusion/</ref> 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.<ref>{{cite web|url=http://www.space.com/23025-doctor-who-tardis-regions-universe.html|title=A Cosmic 'Tardis': What the Universe Has In Common with 'Doctor Who'|work=Space.com}}</ref> 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.<ref name="NS2007" />
+Another type of model, the backreaction conjecture,<ref>{{cite journal | doi = 10.1088/0264-9381/28/16/164008 | volume=28 | title=Backreaction: directions of progress | journal=Classical and Quantum Gravity | pages=164008|arxiv = 1102.0408 |bibcode = 2011CQGra..28p4008R }}</ref><ref>{{cite journal | doi = 10.1146/annurev.nucl.012809.104435 | volume=62 | title=Backreaction in Late-Time Cosmology | journal=Annual Review of Nuclear and Particle Science | pages=57–79|arxiv = 1112.5335 |bibcode = 2012ARNPS..62...57B }}</ref> was proposed by cosmologist Syksy Räsänen:<ref name="NS2007">{{cite news|url=https://www.newscientist.com/article/dn11498-is-dark-energy-an-illusion/|title=Is dark energy an illusion?|date=2007|newspaper=[[New Scientist]]}}</ref> 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.<ref>{{cite web|url=http://www.space.com/23025-doctor-who-tardis-regions-universe.html|title=A Cosmic 'Tardis': What the Universe Has In Common with 'Doctor Who'|work=Space.com}}</ref> 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.<ref name="NS2007" />
 ==Theories for the consequences to the universe==
 {{See also|Future of an expanding universe}}
-As the universe expands, the density of radiation and ordinary and [[dark matter]] declines more quickly than the density of [[dark energy]] (see [[Equation of State (Cosmology)|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]]).<ref name=Ryden/>
+As the universe expands, the density of radiation and ordinary and [[dark matter]] declines more quickly than the density of [[dark energy]] (see [[Equation of state (cosmology)|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]]).<ref name=Ryden/>{{Page needed|date=September 2016}}
-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 space]]time. 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.<ref>{{cite journal|last1=Krauss|first1=Lawrence M.|last2=Scherrer|first2=Robert J.|title=The return of a static universe and the end of cosmology|journal=General Relativity and Gravitation|date=28 June 2007|volume=39|issue=10|pages=1545–1550|doi=10.1007/s10714-007-0472-9|arxiv = 0704.0221 |bibcode = 2007GReGr..39.1545K }}</ref>
+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 space]]time. 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.<ref>{{cite journal|last1=Krauss|first1=Lawrence M.|last2=Scherrer|first2=Robert J.|title=The return of a static universe and the end of cosmology|journal=General Relativity and Gravitation|date=2007-06-28|volume=39|issue=10|pages=1545–1550|doi=10.1007/s10714-007-0472-9|arxiv = 0704.0221 |bibcode = 2007GReGr..39.1545K }}</ref>
 Alternatives for the [[ultimate fate of the universe]] include the [[Big Rip]] mentioned above, a [[Big Bounce]], [[Big Freeze]], or [[Big Crunch]].