Editing Accelerating expansion of the universe

{{short description|Cosmological phenomenon}}
{{cosmology}}
[[File:Lambda-Cold Dark Matter, Accelerated Expansion of the Universe, Big Bang-Inflation.jpg|thumb|upright=1.8|Lambda-CDM, accelerated [[expansion of the universe]]. The timeline in this schematic diagram extends from the [[Big Bang]]/inflation era 13.8&nbsp;billion years ago to the present cosmological time.]]
[[Observational astronomy|Observations]] show that the [[expansion of the universe]] is [[Acceleration (differential geometry)|accelerating]], such that the [[velocity]] at which a distant [[galaxy]] recedes from the observer is continuously increasing with time.<ref name="NYT-20170220">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Cosmos Controversy: The Universe Is Expanding, but How Fast? |url=https://www.nytimes.com/2017/02/20/science/hubble-constant-universe-expanding-speed.html |date=20 February 2017 |work=[[The New York Times]] |access-date=21 February 2017 }}</ref><ref name="AM-20170818">{{cite web |last=Scharping |first=Nathaniel |title=Gravitational Waves Show How Fast The Universe is Expanding |url=http://www.astronomy.com/news/2017/10/gravitational-waves-show-how-fast-the-universe-is-expanding |date=18 October 2017 |website=[[Astronomy (magazine)|Astronomy]] |access-date=18 October 2017 }}</ref><ref name="ES-20180311">{{cite web |last1=Weaver |first1=Donna |last2=Villard |first2=Ray |title=Measuring universe expansion reveals mystery – Is something unpredicted going on in the depths of space? |url=http://earthsky.org/space/measuring-universe-expansion-reveals-mystery |date=11 March 2018 |website=[[Earth & Sky]] |access-date=11 March 2018 }}</ref> The accelerated expansion of the [[universe]] was discovered in 1998 by two independent projects, the [[Supernova Cosmology Project]] and the [[High-Z Supernova Search Team]], which used distant [[type Ia supernovae]] to measure the acceleration.<ref name="BBC">{{cite news |url=https://www.bbc.co.uk/news/science-environment-15165371 |title=Nobel physics prize honours accelerating universe find |work=BBC News |date=2011-10-04}}</ref><ref>{{cite web |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2011/ |title=The Nobel Prize in Physics 2011 |publisher=Nobelprize.org |access-date=2011-10-06}}</ref><ref name="peebles">{{cite journal |author=Peebles |first1=P. J. E. |last2=Ratra |first2=Bharat |s2cid=118961123 |title=The cosmological constant and dark energy |year=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 idea was that as type Ia supernovae have almost the same intrinsic brightness (a [[standard candle]]), and since objects that are further away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological [[redshift]], which measures how much the universe has expanded since the supernova occurred; the [[Hubble law]] established that the further away an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. 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=9780198526827}}</ref> Confirmatory evidence has been found in [[baryon acoustic oscillations]], and in analyses of the [[Galaxy cluster|clustering of galaxies]].

The accelerated expansion of the universe is thought to have begun since the universe entered its [[dark-energy-dominated era]] roughly 5&nbsp;billion years ago.<ref name="Frieman">{{Cite journal |last1=Frieman |first1=Joshua A. |last2=Turner |first2=Michael S. |last3=Huterer |first3=Dragan |s2cid=15117520 |year=2008 |title=Dark Energy and the Accelerating Universe |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(1 + ''w''))</sup>}} (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&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 accelerated 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 standard model of [[physical cosmology|cosmology]], which also includes [[cold dark matter]] (CDM) and is known as the [[Lambda-CDM model]].

==Background==
{{Nature timeline}}
{{Further|Cosmological constant|Lambda-CDM model|Hubble's law|Friedmann–Lemaître–Robertson–Walker metric|Friedmann equations}}
In the decades since the detection of [[cosmic microwave background]] (CMB) in 1965,<ref name="Penzias&Wilson">{{cite journal |last1=Penzias |first1=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|doi-access=free }}</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 display="block"> H^2={\left ( \frac{\dot{a}}{a} \right )}^2=\frac{8{\pi}G}{3}\rho-\frac{{\kappa}c^2}{a^2} </math>
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. |author-link1=Robert J. Nemiroff |last2=Patla |first2=Bijunath |s2cid=51782808 |title=Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations |journal=American Journal of Physics |volume=76 |issue=3 |pages=265–276 |doi=10.1119/1.2830536 |arxiv=astro-ph/0703739 |bibcode=2008AmJPh..76..265N |year=2008}}</ref>

The  [[Critical density (cosmology)|critical density]] is defined as
<math display="block"> \rho_c=\frac{3H^2}{8{\pi}G} </math>
and the [[density parameter]]
<math display="block"> \Omega=\frac{\rho}{\rho_c} </math>

The Hubble parameter can then be rewritten as
<math display="block"> 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>{{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=978-0521518888|bibcode=2010deot.book.....R }}</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
<math display="block"> \frac{\ddot{a}}{a}=-\frac{4{\pi}G}{3}\left( \rho + \frac{3P}{c^2} \right) </math>
where the [[pressure]] {{mvar|P}} is defined by the cosmological model chosen. (see [[Accelerating universe#Explanatory models|explanatory models]])

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 |last=Ryden |first=Barbara |title=Introduction to Cosmology |date=2003 |publisher=Addison Wesley |isbn=978-0-8053-8912-8 |location=San Francisco, California |pages=103 |language=en-us}}</ref> Recent observations indicate this deceleration parameter is negative.

===Relation to inflation===
According to the theory of [[Inflation (cosmology)|cosmic inflation]], the very early universe underwent a period of very rapid, quasi-exponential expansion. While the time-scale for this period of expansion was far shorter than that of the existing expansion, this was a period of accelerated expansion with some similarities to the current epoch.

===Technical definition===
The definition of "accelerating expansion" is that the second time derivative of the cosmic scale factor, <math> \ddot{a} </math>, is positive, which is equivalent to the [[deceleration parameter]], <math>q</math>, being negative. However, note this does '''not''' imply that the [[Hubble constant|Hubble parameter]] is increasing with time. Since the Hubble parameter is defined as <math> H(t) \equiv \dot{a}(t) / a(t) </math>, it follows from the definitions that the derivative of the Hubble parameter is given by
<math display="block"> \frac{dH}{dt} = -H^2(1 + q) </math>
so the Hubble parameter is decreasing with time unless <math> q < -1 </math>. Observations prefer <math> q \approx -0.55 </math>, which implies that <math> \ddot{a} </math> is positive but <math> dH/dt </math> is negative. Essentially, this implies that the cosmic recession velocity of any one particular galaxy is increasing with time, but its velocity/distance ratio is still decreasing; thus different galaxies expanding across a sphere of fixed radius cross the sphere more slowly at later times.

It is seen from above that the case of "zero acceleration/deceleration" corresponds to <math> a(t)</math> is a linear function of <math>t</math>, <math> q = 0 </math>, <math> \dot{a} = const</math>, and <math> H(t) = 1/t </math>.

==Evidence for acceleration==
The rate of expansion of the universe can be analyzed using the [[Magnitude (astronomy)|magnitude]]-redshift relationship of astronomical objects using [[Cosmic distance ladder#Standard candles|standard candles]], or their distance-redshift relationship using [[standard ruler]]s. Also a factor is the growth of [[large-scale structure of the universe|large-scale structure]], finding that the observed values of the cosmological parameters are best described by models which include an accelerating expansion.

===Supernova observation===
[[File:Asymmetric Ashes (artist's impression).jpg|thumb|right|upright=1|Artist's impression of a Type Ia supernova, as revealed by spectro-polarimetry observations]]

In 1998, the first evidence for acceleration came from the observation of [[Type Ia supernova]]e, which are exploding [[white dwarf]] stars that have exceeded their [[Chandrasekhar limit|stability limit]]. Because they all have similar masses, their intrinsic [[luminosity]] can be standardized. 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).<ref>{{cite arXiv |last1=Albrecht|first1=Andreas |display-authors=etal |title=Report of the Dark Energy Task Force |date=2006 |eprint=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 computer 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 display="block"> a(t)=\frac{1}{1+z} </math>

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 the case of accelerated expansion, <math> \ddot{a} </math> is positive; therefore, <math> \dot{a} </math> was smaller in the past than today. Thus, an accelerating universe took a longer time to expand from 2/3 to 1 times its present size, compared to a non-accelerating universe with constant <math> \dot{a} </math> and the same present-day value of the Hubble constant. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations. [[Adam Riess]] ''et al.'' found that "the distances of the high-redshift SNe Ia were, on average, 10% to 15% further 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. |s2cid=15640044 |display-authors=etal |title=Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant |journal=The Astronomical Journal |volume=116 |issue=3 |pages=1009–1038 |year=1998 |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 |last1=Pain |first1=Reynald |last2=Astier |first2=Pierre |s2cid=119301091 |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 |bibcode=2012CRPhy..13..521A |citeseerx=10.1.1.747.3792}}</ref>

Several researchers have questioned the majority opinion on the acceleration or the assumption of the "[[cosmological principle]]" (that the universe is homogeneous and isotropic).<ref>{{cite journal |last1=Lawton |first1=Thomas |date=April 30, 2022 |title=Controversial claim that the universe is skewed could upend cosmology |url=https://www.newscientist.com/article/mg25433840-900-controversial-claim-that-the-universe-is-skewed-could-upend-cosmology/ |journal=New Scientist}}</ref> For example, a 2019 paper analyzed the [[Joint Light-curve Analysis]] catalog of Type Ia supernovas, containing ten times as many supernova as were used in the 1998 analyses, and concluded that there was little evidence for a "monopole", that is, for an isotropic acceleration in all directions.<ref>{{cite journal |first1=Jacques |last1=Colin|first2= Roya|last2= Mohayaee|first3= Mohamed |last3=Rameez|first4= Subir|last4= Sarkar |title=Evidence for anisotropy of cosmic acceleration⋆ |journal=Astronomy & Astrophysics |date=Nov 2019 |volume=631 |pages=L13 |doi=10.1051/0004-6361/201936373 |arxiv=1808.04597 |bibcode=2019A&A...631L..13C |s2cid=208175643 |url=https://www.aanda.org/articles/aa/full_html/2019/11/aa36373-19/aa36373-19.html}}</ref><ref>{{cite journal |last1=Sarkar |first1=Subir |date=Mar 2022 |title=Heart of Darkness |url=https://inference-review.com/article/heart-of-darkness |journal=Inference |volume=6 |issue=4 |doi=10.37282/991819.22.21 |s2cid=247890823 |doi-access=free}}</ref> See also the section on [[#Alternative theories|Alternate theories]] below.

===Baryon acoustic oscillations===
{{Main|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. |s2cid=3629998 |year=2009 |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 |issue=2 |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 inhomogeneities 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 {{nowrap|100 ''h''<sup>−1</sup> [[Parsec#Megaparsecs and gigaparsecs|Mpc]]}},<ref name=Bassett/> (where ''h'' is the [[dimensionless Hubble constant]]) 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 the accelerated expansion of the universe.<ref>{{cite journal |last1=Eisenstein |first1=Daniel J. |s2cid=4834543 |display-authors=etal |title=Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies |journal=The Astrophysical Journal |year=2005 |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 {{explain|date=March 2018}}.<ref>{{cite book |last=Dekel |first=Avishai |title=Formation of Structure in the Universe |date=1999 |publisher=Cambridge University Press |isbn=9780521586320 |location=New York, New York}}</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===
{{See also|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.

<math display="block"> 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/>

===Gravitational waves as standard sirens===
Recent discoveries of [[gravitational wave]]s through [[LIGO]] and [[Virgo interferometer|VIRGO]]<ref name=":0">{{Cite journal|author1=((The LIGO Scientific Collaboration and The Virgo Collaboration))|author2=((The 1M2H Collaboration))|author3=((The Dark Energy Camera GW-EM Collaboration and the DES Collaboration))|author4=((The DLT40 Collaboration))|author5=((The Las Cumbres Observatory Collaboration))|author6=((The VINROUGE Collaboration))|author7=((The MASTER Collaboration))|s2cid=205261622|date=2017-11-02|title=A gravitational-wave standard siren measurement of the Hubble constant|url=http://man.ac.uk/g4Y4sF|journal=Nature|volume=551|issue=7678|pages=85–88|arxiv=1710.05835|bibcode=2017Natur.551...85A|doi=10.1038/nature24471|issn=0028-0836|pmid=29094696}}</ref><ref>{{Cite journal |last1=Abbott |first1=B. P. |s2cid=119286014 |collaboration=LIGO Scientific Collaboration and Virgo Collaboration |date=2016-02-11 |title=Observation of Gravitational Waves from a Binary Black Hole Merger |journal=Physical Review Letters |volume=116 |issue=6 |pages=061102 |doi=10.1103/PhysRevLett.116.061102 |pmid=26918975 |arxiv=1602.03837 |bibcode=2016PhRvL.116f1102A}}</ref><ref name=":1">{{Cite journal |last=ur Rahman |first=Syed Faisal |date=2018-04-01 |title=Where next for the expanding universe? |journal=Astronomy & Geophysics |language=en |volume=59 |issue=2 |pages=2.39–2.42 |doi=10.1093/astrogeo/aty088 |issn=1366-8781 |bibcode=2018A&G....59b2.39F}}</ref> not only confirmed Einstein's predictions but also opened a new window into the universe. These gravitational waves can work as sort of [[standard siren]]s to measure the expansion rate of the universe. Abbot et al. 2017 measured the Hubble constant value to be approximately 70 kilometres per second per megaparsec.<ref name=":0" /> The amplitudes of the strain 'h' is dependent on the masses of the objects causing waves, distances from observation point and gravitational waves detection frequencies. The associated distance measures are dependent on the cosmological parameters like the Hubble Constant for nearby objects<ref name=":0" /> and will be dependent on other cosmological parameters like the dark energy density, matter density, etc. for distant sources.<ref>{{Cite journal |last1=Rosado |first1=Pablo A. |last2=Lasky |first2=Paul D. |last3=Thrane |first3=Eric |last4=Zhu |first4=Xingjiang |last5=Mandel |first5=Ilya |last6=Sesana |first6=Alberto |s2cid=8736504 |year=2016 |title=Detectability of Gravitational Waves from High-Redshift Binaries |journal=Physical Review Letters |volume=116 |issue=10 |pages=101102 |doi=10.1103/PhysRevLett.116.101102 |pmid=27015470 |arxiv=1512.04950 |bibcode=2016PhRvL.116j1102R}}</ref><ref name=":1" />

==Explanatory models==
[[File:Dark Energy.jpg|thumb|right|upright=2|The expansion of the Universe accelerating. Time flows from bottom to top]]

===Dark energy===
{{Main|Dark energy}}
The most important property of dark energy is that it has negative pressure (repulsive action) which is distributed relatively homogeneously in space.

<math display="block"> P=wc^2\rho </math>
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 expansion of the universe#Background|acceleration equation]] above).

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 ''et al.'' found that their results from supernova observations favoured expanding models with positive cosmological constant ({{math|''Ω<sub>λ</sub>'' > 0}}) and an accelerated expansion ({{math|''q''<sub>0</sub> < 0}}).<ref name=Riess/>

===Phantom energy===
{{Main|Phantom energy}}
These 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 |s2cid=119498512 |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. |s2cid=9820570 |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 |year=2002 |pages=23–29 |doi=10.1016/S0370-2693(02)02589-3 |arxiv=astro-ph/9908168 |bibcode=2002PhLB..545...23C }}</ref>

===Alternative theories===
{{See also|Dark energy#Theories of dark energy|Dark energy#Alternatives to dark energy}}

There are many alternative explanations for the accelerating universe. Some examples are [[quintessence (physics)|quintessence]], a proposed form of dark energy with a non-constant state equation, whose density decreases with time. A [[negative mass]] cosmology does not assume that the mass density of the universe is positive (as is done in supernova observations), and instead finds a negative cosmological constant. [[Occam's razor]] also suggests that this is the 'more parsimonious hypothesis'.<ref name="EA-20181205">{{cite web |author=University of Oxford |title=Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos |url=https://www.eurekalert.org/pub_releases/2018-12/uoo-bbt120318.php |date=5 December 2018 |work=[[EurekAlert!]] |access-date=6 December 2018 |author-link=University of Oxford }}</ref><ref name="ARX-2018">{{cite journal |last=Farnes |first=J.S. |s2cid=53600834 |title=A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ΛCDM Framework |journal=Astronomy & Astrophysics |volume=620 |pages=A92 |arxiv=1712.07962 |year=2018 |doi=10.1051/0004-6361/201832898 |bibcode=2018A&A...620A..92F }}</ref> [[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 |s2cid=14155129 |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 |pages=1–13 |bibcode=2008ApJS..177....1H }}</ref> Alternatively, some authors have argued that the accelerated expansion of the universe 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 |s2cid=119232871 |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 |issue=78 |page=A78 |year=2012 |doi=10.1051/0004-6361/201016103 |arxiv=1110.3054 |bibcode=2012A&A...537A..78B }}{{open access}}</ref><ref name="Hajdukovic">{{cite journal |first=D. S. |last=Hajduković |s2cid=119257686 |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 |pages=1–5 |date=2012 |arxiv=1201.4594 |bibcode=2012Ap&SS.339....1H |url=https://cds.cern.ch/record/1418593}}</ref><ref name="villata13">{{cite journal |first=M. |last=Villata |s2cid=119288465 |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 |issue=1 |pages=1–9 |arxiv=1302.3515 |bibcode=2013Ap&SS.345....1V }}</ref> or a deviation of the gravitational laws from general relativity, such as [[massive gravity]], meaning that gravitons themselves have mass.<ref>{{cite news|url=https://www.theguardian.com/science/2020/jan/25/has-physicists-gravity-theory-solved-impossible-dark-energy-riddle|title=Has physicist's gravity theory solved 'impossible' dark energy riddle?|last=Devlin|first=Hannah|work=The Guardian|date=January 25, 2020}}</ref> The measurement of the speed of gravity with the gravitational wave event [[GW170817]] ruled out many modified gravity theories as alternative explanations to dark energy.<ref>{{Cite journal |title=Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure |journal=Physics Letters B |volume=765 |issue=382 |pages=382–385 |first1=Lucas |last1=Lombriser |first2=Nelson |last2=Lima |s2cid=118486016 |arxiv=1602.07670 |year=2017 |doi=10.1016/j.physletb.2016.12.048|bibcode=2017PhLB..765..382L }}</ref><ref>{{cite news |url=https://phys.org/news/2017-02-quest-riddle-einstein-theory.html |title=Quest to settle riddle over Einstein's theory may soon be over |date=February 10, 2017 |access-date=October 29, 2017 |website=[[phys.org]]}}</ref><ref>{{cite news |url=https://arstechnica.co.uk/science/2017/02/theoretical-battle-dark-energy-vs-modified-gravity/ |title=Theoretical battle: Dark energy vs. modified gravity |date=February 25, 2017 |access-date=October 27, 2017 |website=[[Ars Technica]]}}</ref> Another type of model, the backreaction conjecture,<ref>{{cite journal |doi=10.1088/0264-9381/28/16/164008 |volume=28 |issue=16 |title=Backreaction: directions of progress |journal=Classical and Quantum Gravity |pages=164008 |arxiv=1102.0408 |bibcode=2011CQGra..28p4008R |last1=Räsänen |first1=Syksy |last2=Ratra |first2=Bharat |s2cid=118485681 |year=2011 }}</ref><ref>{{cite journal |doi=10.1146/annurev.nucl.012809.104435| doi-access=free |volume=62 |issue=1 |title=Backreaction in Late-Time Cosmology |journal=[[Annual Review of Nuclear and Particle Science]] |pages=57–79 |arxiv=1112.5335 |bibcode=2012ARNPS..62...57B |last1=Buchert |first1=Thomas |last2=Räsänen |first2=Syksy |s2cid=118798287 |year=2012 }}</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 Earth is 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 slowed 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 undergoing an accelerated expansion.<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' |website=Space.com|date=October 2013 }}</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" />

[[Shockwave cosmology]], proposed by Joel Smoller and Blake Temple in 2003, has the “big bang” as an explosion inside a black hole, producing the expanding volume of space and matter that includes the observable universe.<ref>{{Cite journal |last=Smoller |first=Joel |last2=Temple |first2=Blake |date=2003-09-30 |title=Shock-wave cosmology inside a black hole |url=https://pnas.org/doi/full/10.1073/pnas.1833875100 |journal=Proceedings of the National Academy of Sciences |language=en |volume=100 |issue=20 |pages=11216–11218 |doi=10.1073/pnas.1833875100 |issn=0027-8424|arxiv=astro-ph/0210105 }}</ref> A related theory by Smoller, Temple, and Vogler proposes that this shockwave may have resulted in our part of the universe having a lower density than that surrounding it, causing the accelerated expansion normally attributed to dark energy.<ref name=":3">{{Cite web |last=published |first=Clara Moskowitz |date=2009-08-17 |title='Big Wave' Theory Offers Alternative to Dark Energy |url=https://www.space.com/7145-big-wave-theory-offers-alternative-dark-energy.html |access-date=2025-05-25 |website=Space |language=en}}</ref><ref name=":2">{{Cite journal |last=Smoller |first=Joel |last2=Temple |first2=Blake |last3=Vogler |first3=Zeke |date=November 2017 |title=An instability of the standard model of cosmology creates the anomalous acceleration without dark energy |url=https://royalsocietypublishing.org/doi/10.1098/rspa.2016.0887 |journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |language=en |volume=473 |issue=2207 |pages=20160887 |doi=10.1098/rspa.2016.0887 |issn=1364-5021|pmc=5719618 }}</ref> They also propose that this related theory could be tested: a universe with dark energy should give a figure for the cubic correction to redshift versus luminosity C = −0.180 at a = a whereas for Smoller, Temple, and Vogler's alternative C should be positive rather than negative. They give a more precise calculation for their shockwave model alternative as: the cubic correction to redshift versus luminosity at a = a is C = 0.359.<ref name=":2" />

Although shockwave cosmology produces a universe that "looks essentially identical to the aftermath of the big bang",<ref>{{Cite book |last=Barnes |first=Luke A. |title=The cosmic revolutionary's handbook: or: how to beat the big bang |last2=Lewis |first2=Geraint F. |date=2020 |publisher=Cambridge University Press |isbn=978-1-108-76209-0 |location=Cambridge}}</ref> cosmologists consider that it needs further development before it could be considered as a more advantageous model than the big bang theory (or standard model) in explaining the universe. In particular, and especially for the proposed alternative to dark energy, it would need to explain big bang nucleosynthesis, the quantitative details of the microwave background anisotropies, the Lyman-alpha forest, and galaxy surveys.<ref name=":3" />

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.<ref>{{cite journal |last=Wiltshire |first=David L. |s2cid=1152275 |year=2007 |title=Exact Solution to the Averaging Problem in Cosmology |journal=Physical Review Letters |volume=99 |issue=25 |page=251101 |doi=10.1103/PhysRevLett.99.251101 |pmid=18233512 |bibcode=2007PhRvL..99y1101W |arxiv=0709.0732 }}</ref><ref>{{cite journal |author1=Ishak, Mustapha |author2=Richardson, James |author3=Garred, David |author4=Whittington, Delilah |author5=Nwankwo, Anthony |author6=Sussman, Roberto |s2cid=118801032 |doi=10.1103/PhysRevD.78.123531 |journal=Physical Review D |title=Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW? |volume=78 |issue=12 |pages=123531 |year=2008 |arxiv=0708.2943 |bibcode=2008PhRvD..78l3531I}}</ref><ref>{{cite journal |author1=Mattsson, Teppo |s2cid=14226736 |doi=10.1007/s10714-009-0873-z |journal=General Relativity and Gravitation |volume=42 |title=Dark energy as a mirage |issue=3 |pages=567–599 |year=2010 |arxiv=0711.4264 |bibcode=2010GReGr..42..567M}}</ref><ref>{{cite journal |last=Clifton |first=Timothy |author2=Ferreira, Pedro |date=April 2009 |title=Does Dark Energy Really Exist? |journal=Scientific American |volume=300 |issue=4 |pages=48–55 |doi=10.1038/scientificamerican0409-48 |pmid=19363920 |bibcode=2009SciAm.300d..48C }}</ref> 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 (astronomy)|Hubble bubble]].<ref>{{Cite journal |doi=10.1103/PhysRevD.78.084032 |arxiv=0809.1183 |title=Cosmological equivalence principle and the weak-field limit |journal=Physical Review D |volume=78 |issue=8 |pages=084032 |year=2008 |last1=Wiltshire |first1=D. |s2cid=53709630 |bibcode=2008PhRvD..78h4032W}}</ref><ref>{{cite web |last=Gray |first=Stuart |title=Dark questions remain over dark energy |url=http://www.abc.net.au/science/articles/2009/12/09/2765371.htm |publisher=ABC Science Australia |access-date=27 January 2013|date=2009-12-08 }}</ref><ref>{{cite news |last=Merali |first=Zeeya |title=Is Einstein's Greatest Work All Wrong—Because He Didn't Go Far Enough? |url=http://discovermagazine.com/2012/mar/09-is-einsteins-greatest-work-wrong-didnt-go-far |access-date=27 January 2013 |newspaper=Discover magazine |date=March 2012}}</ref> 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,<ref>Wolchover, Natalie (27 September 2011) [https://web.archive.org/web/20200924002445/http://www.nbcnews.com/id/44690771 'Accelerating universe' could be just an illusion], NBC News</ref><ref>{{cite journal |last=Tsagas |first=Christos G. |s2cid=119179171 |title=Peculiar motions, accelerated expansion, and the cosmological axis |journal=Physical Review D |year=2011 |volume=84 |issue=6 |pages=063503 |doi=10.1103/PhysRevD.84.063503 |bibcode=2011PhRvD..84f3503T |arxiv=1107.4045 }}</ref> or that the supernova sample size used wasn't large enough.<ref name="sarkar">{{cite journal |last1=Nielsen |first1=J. T. |last2=Guffanti |first2=A. |last3=Sarkar |first3=S. |year=2016 |title=Marginal evidence for cosmic acceleration from Type Ia supernovae |journal=Scientific Reports |volume=6 |issue=35596 |page=35596 |arxiv=1506.01354 |bibcode=2016NatSR...635596N |doi=10.1038/srep35596 |pmc=5073293 |pmid=27767125}}</ref><ref name="ox.ac.uk">{{cite web |author=Gillespie |first=Stuart |date=21 October 2016 |title=The universe is expanding at an accelerating rate – or is it? |url=http://www.ox.ac.uk/news/science-blog/universe-expanding-accelerating-rate-–-or-it |website=University of Oxford – News & Events – Science Blog ([[WP:NEWSBLOG]])}}</ref>

==Consequences for the universe==
{{See also|Future of an expanding universe}}
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 (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 the [[cosmological constant]]).<ref name=Ryden/>

In models where dark energy is the cosmological constant, the universe will expand exponentially with time in the far future, coming closer and closer to a [[de Sitter universe]]. 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 existing age, leading to the end of any life as the distant universe turns dark.<ref>{{cite journal |last1=Krauss |first1=Lawrence M. |last2=Scherrer |first2=Robert J. |s2cid=123442313 |title=The return of a static universe and the end of cosmology |journal=General Relativity and Gravitation |year=2007 |volume=39 |issue=10 |pages=1545–1550 |doi=10.1007/s10714-007-0472-9 |arxiv=0704.0221 |bibcode=2007GReGr..39.1545K }}</ref>

A constantly expanding universe with a non-zero cosmological constant has mass density decreasing over time. Under such a scenario, it is understood that all matter will ionize and disintegrate into isolated stable particles such as [[electrons]] and [[neutrinos]], with all complex structures dissipating.<ref>[[John Baez]], "The End of the Universe", 7 February 2016. http://math.ucr.edu/home/baez/end.html</ref> This is called "[[heat death of the universe]]" (or the [[Big Freeze]]).

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

==See also==<!-- Please respect alphabetical order -->
{{cols|colwidth=20em}}
*[[Cosmological constant]]
*[[Friedmann–Lemaître–Robertson–Walker metric]]
*[[High-Z Supernova Search Team]]
*[[Lambda-CDM model]]
*[[List of multiple discoveries#21st century|List of multiple discoveries]]
*[[Expansion of the universe]]
*[[Scale factor (cosmology)]]
*[[Supernova Cosmology Project]]
*[[Hubble constant]]
{{colend}}

==Notes==
{{Reflist|group=notes}}

==References==
{{Reflist|30em}}

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[[Category:Acceleration|Expansion of the universe]]
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