View source for Dark energy

{{Short description|Energy driving the accelerated expansion of the universe}}
{{Distinguish|dark fluid|dark flow|dark matter}}
{{Use dmy dates|date=May 2020}}
{{Cosmology|comp/struct}}
In [[physical cosmology]] and [[astronomy]], '''dark energy''' is an unknown form of [[energy]] that affects the [[universe]] on the largest scales. Its primary effect is to drive the [[accelerating expansion of the universe]]. Assuming that the [[lambda-CDM model]] of cosmology is correct,<ref>{{Cite journal |first1=Anto |last1=Idicherian Lonappan |last2=Kumar |first2=Sumit |first3=Ruchika|last3=R | first4=Anjan |last4=Ananda Sen|date=21 February 2018 |title=Bayesian evidences for dark energy models in light of current observational data |journal=[[Physical Review D]] |volume=97 |issue=4 |page=043524 | arxiv=1707.00603 |doi=10.1103/PhysRevD.97.043524 |bibcode=2018PhRvD..97d3524L |s2cid=119249858 }}</ref> dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day [[observable universe]] while [[dark matter]] and [[Baryon#Baryonic matter|ordinary (baryonic)]] matter contribute 26% and 5%, respectively, and other components such as [[neutrino]]s and [[photon]]s are nearly negligible.<ref name="planck_overview">{{Cite journal |last1=Ade |first1=P. A. R. |last2=Aghanim |first2=N.|author2-link=Nabila Aghanim |last3=Alves |first3=M. I. R. |last4=Armitage-Caplan |first4=C. |last5=Arnaud |first5=M. |last6=Ashdown |first6=M. |last7=Atrio-Barandela |first7=F. |last8=Aumont |first8=J. |last9=Aussel |first9=H. |last10=Baccigalupi |first10=C. |last11=Banday |first11=A. J. |display-authors=3 |date=22 March 2013 |title=Planck 2013 results. I. Overview of products and scientific results – Table 9 |journal=[[Astronomy and Astrophysics]] |volume=571 |pages=A1 |arxiv=1303.5062 |bibcode=2014A&A...571A...1P |doi=10.1051/0004-6361/201321529 |collaboration=Planck Collaboration |last12=Barreiro |first12=R. B. |last13=Barrena |first13=R. |last14=Bartelmann |first14=M. |last15=Bartlett |first15=J. G. |last16=Bartolo |first16=N. |last17=Basak |first17=S. |last18=Battaner |first18=E. |last19=Battye |first19=R. |last20=Benabed |first20=K. |last21=Benoît |first21=A. |last22=Benoit-Lévy |first22=A. |last23=Bernard |first23=J.-P. |last24=Bersanelli |first24=M. |last25=Bertincourt |first25=B. |last26=Bethermin |first26=M. |last27=Bielewicz |first27=P. |last28=Bikmaev |first28=I. |last29=Blanchard |first29=A. |last30=Bobin |first30=J.|s2cid=218716838 }}</ref><ref name="planck_overview2">{{Cite journal |last1=Ade |first1=P. A. R. |last2=Aghanim |first2=N. |author2-link=Nabila Aghanim|last3=Alves |first3=M. I. R. |last4=Armitage-Caplan |first4=C. |last5=Arnaud |first5=M. |last6=Ashdown |first6=M. |last7=Atrio-Barandela |first7=F. |last8=Aumont |first8=J. |last9=Aussel |first9=H. |last10=Baccigalupi |first10=C. |last11=Banday |first11=A. J. |display-authors=3 |date=31 March 2013 |title=Planck 2013 Results Papers |url=http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers |journal=[[Astronomy and Astrophysics]] |volume=571 |pages=A1 |arxiv=1303.5062 |bibcode=2014A&A...571A...1P |doi=10.1051/0004-6361/201321529 |archive-url=https://web.archive.org/web/20130323234553/http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers |archive-date=23 March 2013 |collaboration=Planck Collaboration |last12=Barreiro |first12=R. B. |last13=Barrena |first13=R. |last14=Bartelmann |first14=M. |last15=Bartlett |first15=J. G. |last16=Bartolo |first16=N. |last17=Basak |first17=S. |last18=Battaner |first18=E. |last19=Battye |first19=R. |last20=Benabed |first20=K. |last21=Benoît |first21=A. |last22=Benoit-Lévy |first22=A. |last23=Bernard |first23=J.-P. |last24=Bersanelli |first24=M. |last25=Bertincourt |first25=B. |last26=Bethermin |first26=M. |last27=Bielewicz |first27=P. |last28=Bikmaev |first28=I. |last29=Blanchard |first29=A. |last30=Bobin |first30=J.|s2cid=218716838 }}</ref><ref name="wmap7parameters">{{Cite web |title=First Planck results: the Universe is still weird and interesting |url=https://arstechnica.com/science/2013/03/first-planck-results-the-universe-is-still-weird-and-interesting/ |date=21 March 2013 |access-date=14 June 2017 |archive-date=2 May 2019 |archive-url=https://web.archive.org/web/20190502143413/https://arstechnica.com/science/2013/03/first-planck-results-the-universe-is-still-weird-and-interesting/ |url-status=live }}</ref><ref name="DarkMatter">Sean Carroll, Ph.D., Caltech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2. p. 46. Retrieved 7 October 2013, "...dark energy: A smooth, persistent component of invisible energy, thought to make up about 70 percent of the current energy density of the universe. Dark energy is known to be smooth because it doesn't accumulate preferentially in galaxies and clusters..."</ref> Dark energy's [[Energy density|density]] is very low: {{val|6e-10|u=J/m<sup>3</sup>}} (≈{{val|7e-30|u=g/cm<sup>3</sup>}}), much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.<ref>{{Cite journal |last1=Steinhardt |first1=Paul J. |last2=Turok |first2=Neil |year=2006 |title=Why the cosmological constant is small and positive |journal=Science |volume=312 |issue=5777 |pages=1180–1183 |arxiv=astro-ph/0605173 |bibcode=2006Sci...312.1180S |doi=10.1126/science.1126231 |pmid=16675662 |s2cid=14178620}}</ref><ref>{{Cite web |title=Dark Energy |url=http://hyperphysics.phy-astr.gsu.edu/hbase/astro/dareng.html |website=Hyperphysics |access-date=4 January 2014 |archive-date=27 May 2013 |archive-url=https://web.archive.org/web/20130527105518/http://hyperphysics.phy-astr.gsu.edu/HBASE/astro/dareng.html |url-status=live }}</ref><ref>{{Cite web |title=Dark Matter(Dark Energy) |url=http://ngm.nationalgeographic.com/2015/01/hidden-cosmos/ferris-text |last=Ferris |first=Timothy |date=January 2015 |access-date=10 June 2015 |archive-date=10 June 2015 |archive-url=https://web.archive.org/web/20150610172523/http://ngm.nationalgeographic.com/2015/01/hidden-cosmos/ferris-text |url-status=dead }}</ref>

The first observational evidence for dark energy's existence came from measurements of [[supernova]]e. Type 1A supernovae have constant luminosity, which means they can be used as accurate distance measures. Comparing this distance to the [[redshift]] (which measures the speed at which the supernova is receding) shows that the [[Hubble's law|universe's expansion]] is [[Accelerating universe|accelerating]].<ref name="NYT-20170220">{{Cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=20 February 2017 |title=Cosmos Controversy: The Universe Is Expanding, but How Fast? |work=[[The New York Times]] |url=https://www.nytimes.com/2017/02/20/science/hubble-constant-universe-expanding-speed.html |access-date=21 February 2017 |archive-date=4 April 2019 |archive-url=https://web.archive.org/web/20190404084517/https://www.nytimes.com/2017/02/20/science/hubble-constant-universe-expanding-speed.html |url-status=live }}</ref><ref name="peebles">{{Cite journal |last1=Peebles, P. J. E. |last2=Ratra, Bharat |year=2003 |title=The cosmological constant and dark energy |journal=Reviews of Modern Physics |volume=75 |issue=2 |pages=559–606 |arxiv=astro-ph/0207347 |bibcode=2003RvMP...75..559P |doi=10.1103/RevModPhys.75.559|s2cid=118961123 }}</ref> Prior to this observation, scientists thought that the gravitational attraction of [[matter]] and energy in the universe would cause the universe's expansion to slow over time. Since the discovery of accelerating expansion, [[Dark_energy#Evidence_of_existence|several independent lines of evidence]] have been discovered that support the existence of dark energy. 

The exact nature of dark energy remains a mystery, and explanations abound. The main candidates are a [[cosmological constant]]<ref>{{Cite web |title=Moon findings muddy the water |url=https://www.ft.com/content/493de45a-8bef-11e0-854c-00144feab49a |archive-url=https://web.archive.org/web/20161122153604/https://www.ft.com/content/493de45a-8bef-11e0-854c-00144feab49a |archive-date=22 November 2016 |access-date=21 November 2016}}</ref><ref name="carroll">{{Cite journal |last=Carroll, Sean |author-link=Sean M. Carroll |year=2001 |title=The cosmological constant |url=http://relativity.livingreviews.org/Articles/lrr-2001-1/index.html |journal=Living Reviews in Relativity |volume=4 |issue=1 |pages=1 |arxiv=astro-ph/0004075 |bibcode=2001LRR.....4....1C |doi=10.12942/lrr-2001-1 |pmc=5256042 |pmid=28179856 |archive-url=https://web.archive.org/web/20061013042057/http://relativity.livingreviews.org/Articles/lrr-2001-1/index.html |archive-date=13 October 2006 |access-date=28 September 2006}}</ref> (representing a constant energy density filling space homogeneously) and [[Scalar field theory|scalar fields]] (dynamic quantities having energy densities that vary in time and space) such as [[Quintessence (physics)|quintessence]] or [[Moduli (physics)|moduli]]. A cosmological constant would remain constant across time and space, while scalar fields can vary. Yet other possibilities are interacting dark energy, an observational effect, and cosmological coupling (see the [[Dark_energy#Theories_of_dark_energy|Theories of Dark Energy]] section).

==History of discovery and previous speculation==

===Einstein's cosmological constant===
The "[[cosmological constant]]" is a constant term that can be added to [[Einstein field equations]] of [[general relativity]]. If considered as a "source term" in the field equation, it can be viewed as equivalent to the mass of empty space (which conceptually could be either positive or negative), or "[[vacuum energy]]".

The cosmological constant was first proposed by [[Albert Einstein|Einstein]] as a mechanism to obtain a solution to the gravitational [[field equation]] that would lead to a static universe, effectively using dark energy to balance gravity.<ref name="Einstein">{{Cite arXiv |eprint=1211.6338 |class=physics.hist-ph |author=Harvey, Alex |title=How Einstein Discovered Dark Energy |year=2012}}</ref> Einstein gave the cosmological constant the symbol Λ (capital lambda). Einstein stated that the cosmological constant required that 'empty space takes the role of gravitating [[negative mass]]es which are distributed all over the interstellar space'.<ref>{{Cite web |title=Volume 7: The Berlin Years: Writings, 1918-1921 (English translation supplement) page 31 |url=https://einsteinpapers.press.princeton.edu/vol7-trans/47 |access-date=2023-09-18 |website=einsteinpapers.press.princeton.edu}}</ref><ref>O'Raifeartaigh, C.; O'Keeffe, M.; Nahm, W.; Mitton, S. (2017). 'Einstein's 1917 Static Model of the Universe: A Centennial Review'. Eur. Phys. J. (H) 42: 431–474.</ref>

The mechanism was an example of [[Fine-tuning (physics)|fine-tuning]], and it was later realized that Einstein's static universe would not be stable: local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The [[dynamic equilibrium|equilibrium]] is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. According to Einstein, "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear, thereby causing accelerated expansion.<ref>{{cite web | title=Dark Energy, Dark Matter | website=Science Mission Directorate | url=https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy | access-date=September 17, 2022 | archive-date=5 November 2020 | archive-url=https://web.archive.org/web/20201105231926/https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/ | url-status=dead }}</ref> These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout the universe. Further, observations made by [[Edwin Hubble]] in 1929 showed that the universe appears to be expanding and is not static. Einstein reportedly referred to his failure to predict the idea of a dynamic universe, in contrast to a static universe, as his greatest blunder.<ref>Gamow, George (1970) ''My World Line: An Informal Autobiography''. p. 44: "Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life." – Here the "cosmological term" refers to the cosmological constant in the equations of general relativity, whose value Einstein initially picked to ensure that his model of the universe would neither expand nor contract; if he had not done this he might have theoretically predicted the universal expansion that was first observed by Edwin Hubble.</ref>

===Inflationary dark energy===
[[Alan Guth]] and [[Alexei Starobinsky]] proposed in 1980 that a negative pressure field, similar in concept to dark energy, could drive [[cosmic inflation]] in the very early universe. Inflation postulates that some repulsive force, qualitatively similar to dark energy, resulted in an enormous and exponential expansion of the universe slightly after the [[Big Bang]]. Such expansion is an essential feature of most current models of the Big Bang. However, inflation must have occurred at a much higher (negative) energy density than the dark energy we observe today, and inflation is thought to have completely ended when the universe was just a fraction of a second old. It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was thought to be irrelevant to the current universe.

Nearly all inflation models predict that the total (matter+energy) density of the universe should be very close to the [[Critical density (cosmology)|critical density]]. During the 1980s, most cosmological research focused on models with critical density in matter only, usually 95% [[cold dark matter]] (CDM) and 5% ordinary matter (baryons). These models were found to be successful at forming realistic galaxies and clusters, but some problems appeared in the late 1980s: in particular, the model required a value for the [[Hubble constant]] lower than preferred by observations, and the model under-predicted observations of large-scale galaxy clustering. These difficulties became stronger after the discovery of [[anisotropy]] in the cosmic microwave background by the [[Cosmic Background Explorer|COBE]] spacecraft in 1992, and several modified CDM models came under active study through the mid-1990s: these included the [[Lambda-CDM model]] and a mixed cold/hot dark matter model. The first direct evidence for dark energy came from supernova observations in 1998 of [[deceleration parameter|accelerated expansion]] in [[Adam Riess|Riess]] ''et al.''<ref name="riess" /> and in [[Saul Perlmutter|Perlmutter]] ''et al.'',<ref name="perlmutter" /> and the Lambda-CDM model then became the leading model. Soon after, dark energy was supported by independent observations: in 2000, the [[BOOMERanG experiment|BOOMERanG]] and [[Millimeter Anisotropy eXperiment IMaging Array|Maxima]] cosmic microwave background experiments observed the first [[Baryon acoustic oscillations|acoustic peak]] in the cosmic microwave background, showing that the total (matter+energy) density is close to 100% of critical density. Then in 2001, the [[2dF Galaxy Redshift Survey]] gave strong evidence that the matter density is around 30% of critical. The large difference between these two supports a smooth component of dark energy making up the difference. Much more precise measurements from [[WMAP]] in 2003–2010 have continued to support the standard model and give more accurate measurements of the key parameters.

The term "dark energy", echoing [[Fritz Zwicky]]'s "dark matter" from the 1930s, was coined by [[Michael Turner (cosmologist)|Michael Turner]] in 1998.<ref>The first appearance of the term "dark energy" is in the article with another cosmologist and Turner's student at the time, Dragan Huterer, "Prospects for Probing the Dark Energy via Supernova Distance Measurements", which was posted to the [[ArXiv.org e-print archive]] in [https://arxiv.org/abs/astro-ph/9808133 August 1998] {{Webarchive|url=https://web.archive.org/web/20170622171956/https://arxiv.org/abs/astro-ph/9808133 |date=22 June 2017 }} and published in {{Cite journal |last1=Huterer |first1=D. |last2=Turner |first2=M. |year=1999 |title=Prospects for probing the dark energy via supernova distance measurements |journal=Physical Review D |volume=60 |issue=8 |pages=081301 |arxiv=astro-ph/9808133 |bibcode=1999PhRvD..60h1301H |doi=10.1103/PhysRevD.60.081301|s2cid=12777640 }}, although the manner in which the term is treated there suggests it was already in general use. Cosmologist Saul Perlmutter has credited Turner with coining the term [http://www.lbl.gov/Science-Articles/Archive/dark-energy.html in an article] {{Webarchive|url=https://web.archive.org/web/20060811215815/http://www.lbl.gov/Science-Articles/Archive/dark-energy.html |date=11 August 2006 }} they wrote together with Martin White, where it is introduced in quotation marks as if it were a neologism. {{Cite journal | doi = 10.1103/PhysRevLett.83.670| title = Constraining Dark Energy with Type Ia Supernovae and Large-Scale Structure| journal = Physical Review Letters| volume = 83| issue = 4| pages = 670–673| year = 1999| last1 = Perlmutter | first1 = S. | last2 = Turner | first2 = M. | last3 = White | first3 = M. |arxiv = astro-ph/9901052 |bibcode = 1999PhRvL..83..670P | s2cid = 119427069}}</ref>

===Change in expansion over time===
[[File:Dark Energy.jpg|thumb|right|upright=2|Diagram representing the accelerated expansion of the universe due to dark energy.]]
High-precision measurements of the [[expansion of the universe]] are required to understand how the expansion rate changes over time and space. In general relativity, the evolution of the expansion rate is estimated from the [[shape of the universe|curvature of the universe]] and the cosmological [[equation of state (cosmology)|equation of state]] (the relationship between temperature, pressure, and combined matter, energy, and vacuum energy density for any region of space). Measuring the equation of state for dark energy is one of the biggest efforts in observational cosmology today. Adding the cosmological constant to cosmology's standard [[Friedmann–Lemaître–Robertson–Walker metric|FLRW metric]] leads to the Lambda-CDM model, which has been referred to as the "''standard model of cosmology''" because of its precise agreement with observations.

As of 2013, the Lambda-CDM model is consistent with a series of increasingly rigorous cosmological observations, including the [[Planck spacecraft]] and the Supernova Legacy Survey. First results from the SNLS reveal that the average behavior (i.e., equation of state) of dark energy behaves like Einstein's cosmological constant to a precision of 10%.<ref name="snls">{{Cite journal |last1=Astier, Pierre ([[Supernova Legacy Survey]]) |last2=Guy |last3=Regnault |last4=Pain |last5=Aubourg |last6=Balam |last7=Basa |last8=Carlberg |last9=Fabbro |last10=Fouchez |last11=Hook |display-authors=29 |year=2006 |title=The Supernova legacy survey: Measurement of Ω<sub>M</sub>, Ω<sub>Λ</sub> and W from the first year data set |journal=Astronomy and Astrophysics |volume=447 |issue=1 |pages=31–48 |arxiv=astro-ph/0510447 |bibcode=2006A&A...447...31A |doi=10.1051/0004-6361:20054185 |last12=Howell |last13=Lafoux |last14=Neill |last15=Palanque-Delabrouille |last16=Perrett |last17=Pritchet |last18=Rich |last19=Sullivan |last20=Taillet |last21=Aldering |last22=Antilogus |last23=Arsenijevic |last24=Balland |last25=Baumont |last26=Bronder |last27=Courtois |last28=Ellis |last29=Filiol |last30=Gonçalves|s2cid=119344498 }}</ref> Recent results from the Hubble Space Telescope Higher-Z Team indicate that dark energy has been present for at least 9 billion years and during the period preceding cosmic acceleration.{{citation needed|date=September 2023}}

==Nature==
The nature of dark energy is more hypothetical than that of dark matter, and many things about it remain in the realm of speculation.<ref>{{Cite news |last=Overbye |first=Dennis |date=22 July 2003 |title=Astronomers Report Evidence of 'Dark Energy' Splitting the Universe |work=The New York Times |url=https://www.nytimes.com/2003/07/22/us/astronomers-report-evidence-of-dark-energy-splitting-the-universe.html |access-date=5 August 2015 |archive-date=26 June 2015 |archive-url=https://web.archive.org/web/20150626222313/http://www.nytimes.com/2003/07/22/us/astronomers-report-evidence-of-dark-energy-splitting-the-universe.html |url-status=live }}</ref> Dark energy is thought to be very homogeneous and not [[density|dense]], and is not known to interact through any of the [[fundamental forces]] other than [[gravity]]. Since it is rarefied and un-massive—roughly 10<sup>−27</sup>&nbsp;kg/m<sup>3</sup>—it is unlikely to be detectable in laboratory experiments. The reason dark energy can have such a profound effect on the universe, making up 68% of universal density in spite of being so dilute, is that it is believed to uniformly fill otherwise empty space.

The [[vacuum energy]], that is, the particle-antiparticle pairs generated and mutually annihilated within a time frame in accord with Heisenberg's [[uncertainty principle]] in the energy-time formulation, has been often invoked as the main contribution to dark energy.<ref>{{cite journal
 |year         = 2002
 |title        = The quantum vacuum and the cosmological constant problem
 |url          = http://philsci-archive.pitt.edu/398/
 |journal      = Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
 |volume       = 33
 |pages        = 663–705
 |doi          = 10.1016/S1355-2198(02)00033-3
 |issue        = 4
 |bibcode      = 2002SHPMP..33..663R
 |arxiv        = hep-th/0012253
 |s2cid        = 9007190
 |last1        = Rugh
 |first1       = S.E.
 |last2        = Zinkernagel
 |first2       = H.
 |access-date  = 29 October 2022
 |archive-date = 30 November 2010
 |archive-url  = https://web.archive.org/web/20101130161201/http://philsci-archive.pitt.edu/398/
 |url-status   = live
}}</ref> The [[mass–energy equivalence]] postulated by [[general relativity]] implies that the vacuum energy should exert a [[gravity|gravitational]] force. Hence, the vacuum energy is expected to contribute to the [[cosmological constant]], which in turn impinges on the accelerated [[expansion of the universe]]. However, the [[cosmological constant problem]] asserts that there is a huge disagreement between the observed values of vacuum energy density and the theoretical large value of zero-point energy obtained by [[quantum field theory]]; the problem remains unresolved.

Independently of its actual nature, dark energy would need to have a strong negative pressure to explain the observed [[accelerating universe|acceleration]] of the [[Metric expansion of space|expansion of the universe]]. According to general relativity, the pressure within a substance contributes to its gravitational attraction for other objects just as its mass density does. This happens because the physical quantity that causes matter to generate gravitational effects is the [[stress–energy tensor]], which contains both the energy (or matter) density of a substance and its pressure. In the [[Friedmann–Lemaître–Robertson–Walker metric]], it can be shown that a strong constant negative pressure (''i.e.,'' tension) in all the universe causes an acceleration in the expansion if the universe is already expanding, or a deceleration in contraction if the universe is already contracting. This accelerating expansion effect is sometimes labeled "gravitational repulsion".

===Technical definition===
{{See also|Friedmann equations}}
In standard cosmology, there are three components of the universe: matter, radiation, and dark energy. Matter is anything whose energy density scales with the inverse cube of the scale factor, i.e., {{math|''ρ''&nbsp;∝&nbsp;''a''<sup>−3</sup>}}, while radiation is anything which scales to the inverse fourth power of the scale factor ({{math|''ρ''&nbsp;∝&nbsp;''a''<sup>−4</sup>}}). This can be understood intuitively: for an ordinary particle in a cube-shaped box, doubling the length of an edge of the box decreases the density (and hence energy density) by a factor of eight (2<sup>3</sup>). For radiation, the decrease in energy density is greater, because an increase in spatial distance also causes a redshift.<ref>{{Cite web |last=Baumann |first=Daniel |title=Cosmology: Part III Mathematical Tripos, Cambridge University |url=http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf |archive-url=https://web.archive.org/web/20170202065045/http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf |archive-date=2 February 2017 |access-date=31 January 2017 |page=21−22}}</ref>

The final component is dark energy: it is an intrinsic property of space and has a constant energy density, regardless of the dimensions of the volume under consideration ({{math|''ρ''&nbsp;∝&nbsp;''a''<sup>0</sup>}}). Thus, unlike ordinary matter, it is not diluted by the expansion of space.

==Evidence of existence==
The evidence for dark energy is indirect but comes from three independent sources:
* Distance measurements and their relation to [[redshift]], which suggest the universe has expanded more in the latter half of its life.<ref name="Durrer">{{Cite journal |last=Durrer, R. |year=2011 |title=What do we really know about Dark Energy? |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |volume=369 |issue=1957 |pages=5102–5114 |arxiv=1103.5331 |bibcode=2011RSPTA.369.5102D |doi=10.1098/rsta.2011.0285 |pmid=22084297 |s2cid=17562830 |author-link1=Ruth Durrer}}</ref>
* The theoretical need for a type of additional energy that is not matter or dark matter to form the [[observationally flat universe]] (absence of any detectable global curvature).
* Measures of large-scale wave patterns of mass density in the universe.

===Supernovae===
<!--This is the plural form of 'supernova'-->
[[File:SN1994D.jpg|thumb|upright=1|A Type Ia supernova (bright spot on the bottom-left) near [[NGC 4526]]]]
In 1998, the [[High-Z Supernova Search Team]]<ref name="riess">{{Cite journal |last1=Riess, Adam G. |author-link=Adam Riess |last2=Filippenko |last3=Challis |last4=Clocchiatti |last5=Diercks |last6=Garnavich |last7=Gilliland |last8=Hogan |last9=Jha |last10=Kirshner |last11=Leibundgut |year=1998 |title=Observational evidence from supernovae for an accelerating universe and a cosmological constant |journal=Astronomical Journal |volume=116 |issue=3 |pages=1009–1038 |arxiv=astro-ph/9805201 |bibcode=1998AJ....116.1009R |bibcode-access=free |doi=10.1086/300499 |doi-access=free |last12=Phillips |last13=Reiss |last14=Schmidt |last15=Schommer |last16=Smith |last17=Spyromilio |last18=Stubbs |last19=Suntzeff |last20=Tonry|s2cid=15640044 |s2cid-access=free |url=https://iopscience.iop.org/article/10.1086/300499/pdf |url-status=live |archive-url=https://archive.today/20231214014649/https://iopscience.iop.org/article/10.1086/300499/pdf |archive-date= 14 Dec 2023 }}</ref> published observations of [[Type Ia supernova|Type Ia]] ("one-A") [[supernova]]e. In 1999, the [[Supernova Cosmology Project]]<ref name="perlmutter">{{Cite journal |last1=Perlmutter, S. |author-link=Saul Perlmutter |last2=Aldering |last3=Goldhaber |last4=Knop |last5=Nugent |last6=Castro |last7=Deustua |last8=Fabbro |last9=Goobar |last10=Groom |last11=Hook |display-authors=29 |year=1999 |title=Measurements of Omega and Lambda from 42 high redshift supernovae |journal=Astrophysical Journal |volume=517 |issue=2 |pages=565–586 |arxiv=astro-ph/9812133 |bibcode=1999ApJ...517..565P |bibcode-access=free |url=https://iopscience.iop.org/article/10.1086/307221/pdf |doi=10.1086/307221 |doi-access=free |last12=Kim |last13=Kim |last14=Lee |last15=Nunes |last16=Pain |last17=Pennypacker |last18=Quimby |last19=Lidman |last20=Ellis |last21=Irwin |last22=McMahon |last23=Ruiz-Lapuente |last24=Walton |last25=Schaefer |last26=Boyle |last27=Filippenko |last28=Matheson |last29=Fruchter |last30=Panagia|s2cid=118910636 |url-status=live |archive-url=https://web.archive.org/web/20231029165856/https://iopscience.iop.org/article/10.1086/307221/pdf |archive-date= Oct 29, 2023 }}</ref> followed by suggesting that the expansion of the universe is [[Deceleration parameter|accelerating]].<ref name="paalhorvathlukacs">The first paper, using observed data, which claimed a positive Lambda term was {{Cite journal |last1=Paál |first1=G. |last2=Horváth |first2=I. |last3=Lukács |first3=B. |display-authors=1 |year=1992 |title=Inflation and compactification from galaxy redshifts? |journal=Astrophysics and Space Science |volume=191 |issue=1 |pages=107–124 |bibcode=1992Ap&SS.191..107P |doi=10.1007/BF00644200|s2cid=116951785 }}</ref> The 2011 [[List of Nobel laureates in Physics|Nobel Prize in Physics]] was awarded to [[Saul Perlmutter]], [[Brian P. Schmidt]], and [[Adam G. Riess]] for their leadership in the discovery.<ref name="N11">{{Cite web |title=The Nobel Prize in Physics 2011 |url=http://nobelprize.org/nobel_prizes/physics/laureates/2011/index.html |publisher=Nobel Foundation |access-date=4 October 2011 |archive-date=1 August 2012 |archive-url=https://web.archive.org/web/20120801221425/http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/index.html |url-status=live }}</ref><ref>[https://www.nobelprize.org/nobel_prizes/physics/laureates/2011/press.html The Nobel Prize in Physics 2011] {{Webarchive|url=https://web.archive.org/web/20111004182642/https://www.nobelprize.org/nobel_prizes/physics/laureates/2011/press.html |date=4 October 2011 }}. Perlmutter got half the prize, and the other half was shared between Schmidt and Riess.</ref>

Since then, these observations have been corroborated by several independent sources. Measurements of the [[cosmic microwave background]], [[gravitational lens]]ing, and the [[large-scale structure of the cosmos]], as well as improved measurements of supernovae, have been consistent with the [[Lambda-CDM model]].<ref name="wmap">{{Cite journal |last=Spergel, D. N. |date=June 2007 |title=Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology |url=https://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/64897.web.pdf |journal=The Astrophysical Journal Supplement Series |volume=170 |issue=2 |arxiv=astro-ph/0603449 |bibcode=2007ApJS..170..377S |citeseerx=10.1.1.472.2550 |doi=10.1086/513700 |collaboration=WMAP collaboration |pages=377–408 |s2cid=1386346 |access-date=26 December 2019 |archive-date=6 April 2020 |archive-url=https://web.archive.org/web/20200406111848/https://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/64897.web.pdf |url-status=live }}</ref> Some people argue that the only indications for the existence of dark energy are observations of distance measurements and their associated redshifts. Cosmic microwave background anisotropies and baryon acoustic oscillations serve only to demonstrate that distances to a given redshift are larger than would be expected from a "dusty" Friedmann–Lemaître universe and the local measured Hubble constant.<ref name="durrer">{{Cite journal |last=Durrer, R. |year=2011 |title=What do we really know about dark energy? |journal=[[Philosophical Transactions of the Royal Society A]] |volume=369 |issue=1957 |pages=5102–5114 |arxiv=1103.5331 |bibcode=2011RSPTA.369.5102D |doi=10.1098/rsta.2011.0285 |pmid=22084297|s2cid=17562830 }}</ref>

Supernovae are useful for cosmology because they are excellent [[standard candle]]s across cosmological distances. They allow researchers to measure the expansion history of the universe by looking at the relationship between the distance to an object and its [[redshift]], which gives how fast it is receding from us. The relationship is roughly linear, according to [[Hubble's law]]. It is relatively easy to measure redshift, but finding the distance to an object is more difficult. Usually, astronomers use standard candles: objects for which the intrinsic brightness, or [[absolute magnitude]], is known. This allows the object's distance to be measured from its actual observed brightness, or [[apparent magnitude]]. Type Ia supernovae are the best-known standard candles across cosmological distances because of their extreme and consistent [[luminosity]].

Recent observations of supernovae are consistent with a universe made up 71.3% of dark energy and 27.4% of a combination of [[dark matter]] and [[Baryon|baryonic matter]].<ref name="Kowalski2008">{{Cite journal |last1=Kowalski |first1=Marek |last2=Rubin, David |last3=Aldering |first3=G. |last4=Agostinho |first4=R. J. |last5=Amadon |first5=A. |last6=Amanullah |first6=R. |last7=Balland |first7=C. |last8=Barbary |first8=K. |last9=Blanc |first9=G. |last10=Challis |first10=P. J. |last11=Conley |first11=A. |display-authors=29 |date=27 October 2008 |title=Improved Cosmological Constraints from New, Old and Combined Supernova Datasets |journal=[[The Astrophysical Journal]] |volume=686 |issue=2 |pages=749–778 |arxiv=0804.4142 |bibcode=2008ApJ...686..749K |doi=10.1086/589937 |last12=Connolly |first12=N. V. |last13=Covarrubias |first13=R. |last14=Dawson |first14=K. S. |last15=Deustua |first15=S. E. |last16=Ellis |first16=R. |last17=Fabbro |first17=S. |last18=Fadeyev |first18=V. |last19=Fan |first19=X. |last20=Farris |first20=B. |last21=Folatelli |first21=G. |last22=Frye |first22=B. L. |last23=Garavini |first23=G. |last24=Gates |first24=E. L. |last25=Germany |first25=L. |last26=Goldhaber |first26=G. |last27=Goldman |first27=B. |last28=Goobar |first28=A. |last29=Groom |first29=D. E. |last30=Haissinski |first30=J.|s2cid=119197696 }}. They find a best-fit value of the [[Lambda-CDM model#Parameters|dark energy density]], Ω<sub>Λ</sub> of 0.713+0.027–0.029([[Random error|stat]])+0.036–0.039([[Systematic error|sys]]), of the [[Lambda-CDM model#Parameters|total matter density]], Ω<sub>M</sub>, of 0.274+0.016–0.016(stat)+0.013–0.012(sys) with an [[Equation of state (cosmology)|equation of state parameter]] w of −0.969+0.059–0.063(stat)+0.063–0.066(sys).</ref>

===Large-scale structure===
The theory of [[Observable universe#Large-scale structure|large-scale structure]], which governs the formation of structures in the universe ([[star]]s, [[quasar]]s, [[galaxy|galaxies]] and [[galaxy groups and clusters]]), also suggests that the density of matter in the universe is only 30% of the critical density.

A 2011 survey, the WiggleZ galaxy survey of more than 200,000 galaxies, provided further evidence towards the existence of dark energy, although the exact physics behind it remains unknown.<ref>{{Cite news |date=19 May 2011 |title=New method 'confirms dark energy' |work=BBC News |url=https://www.bbc.co.uk/news/science-environment-13462926 |access-date=21 July 2018 |archive-date=15 June 2018 |archive-url=https://web.archive.org/web/20180615231105/https://www.bbc.co.uk/news/science-environment-13462926 |url-status=live }}</ref><ref name=real/> The WiggleZ survey from the [[Australian Astronomical Observatory]] scanned the galaxies to determine their redshift. Then, by exploiting the fact that [[baryon acoustic oscillations]] have left [[Void (astronomy)|voids]] regularly of ≈150 Mpc diameter, surrounded by the galaxies, the voids were used as standard rulers to estimate distances to galaxies as far as 2,000 Mpc (redshift 0.6), allowing for accurate estimate of the speeds of galaxies from their redshift and distance. The data confirmed [[cosmic acceleration]] up to half of the age of the universe (7 billion years) and constrain its inhomogeneity to 1 part in 10.<ref name="real">[http://wigglez.swin.edu.au/site/prmay2011a.html Dark energy is real] {{Webarchive|url=https://web.archive.org/web/20110525183818/http://wigglez.swin.edu.au/site/prmay2011a.html |date=25 May 2011 }}, Swinburne University of Technology, 19 May 2011</ref> This provides a confirmation to cosmic acceleration independent of supernovae.

===Cosmic microwave background===
[[File:WMAP 2008 universe content.png|thumb|upright=1.2|Estimated division of total energy in the universe into matter, dark matter and dark energy based on five years of WMAP data.<ref>{{Cite web |title=Content of the Universe – Pie Chart |url=https://map.gsfc.nasa.gov/media/080998/index.html |website=Wilkinson Microwave Anisotropy Probe |publisher=National Aeronautics and Space Administration |access-date=9 January 2018 |archive-date=18 August 2018 |archive-url=https://web.archive.org/web/20180818101057/https://map.gsfc.nasa.gov/media/080998/index.html |url-status=live }}</ref>]]
The existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of [[cosmic microwave background]] [[anisotropy|anisotropies]] indicate that the universe is close to [[flatness problem|flat]]. For the [[shape of the universe]] to be flat, the mass–energy density of the universe must be equal to the [[Friedmann equations#Density parameter|critical density]]. The total amount of matter in the universe (including [[baryon]]s and [[dark matter]]), as measured from the cosmic microwave background spectrum, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%.<ref name="wmap" /> The [[Wilkinson Microwave Anisotropy Probe]] (WMAP) spacecraft [[Wilkinson Microwave Anisotropy Probe#Seven-year data release|seven-year analysis]] estimated a universe made up of 72.8% dark energy, 22.7% dark matter, and 4.5% ordinary matter.<ref name="wmap7parameters" />
Work done in 2013 based on the [[Planck spacecraft]] observations of the cosmic microwave background gave a more accurate estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter.<ref name="Washington Post">{{Cite news |title=Big Bang's afterglow shows universe is 80 million years older than scientists first thought |newspaper=The Washington Post |url=https://www.washingtonpost.com/world/europe/telescope-that-sees-big-bangs-afterglow-sees-older-universe-in-glimpse-of-first-split-second/2013/03/21/ada16076-920e-11e2-9173-7f87cda73b49_story_1.html |access-date=22 March 2013 |archive-url=https://web.archive.org/web/20130322054138/http://www.washingtonpost.com/world/europe/telescope-that-sees-big-bangs-afterglow-sees-older-universe-in-glimpse-of-first-split-second/2013/03/21/ada16076-920e-11e2-9173-7f87cda73b49_story_1.html |archive-date=22 March 2013}}</ref>

===Late-time integrated Sachs–Wolfe effect===
Accelerated cosmic expansion causes [[gravitational potential well]]s and hills to flatten as [[photon]]s pass through them, producing cold spots and hot spots on the cosmic microwave background aligned with vast supervoids and superclusters. This so-called late-time [[Integrated Sachs–Wolfe effect|Integrated Sachs–Wolfe effect (ISW)]] is a direct signal of dark energy in a flat universe.<ref>{{Cite journal |last1=Crittenden |last2=Neil Turok |year=1996 |title=Looking for $\Lambda$ with the Rees-Sciama Effect |journal=Physical Review Letters |volume=76 |issue=4 |pages=575–578 |arxiv=astro-ph/9510072 |bibcode=1996PhRvL..76..575C |doi=10.1103/PhysRevLett.76.575 |pmid=10061494|s2cid=119012700 }}</ref> It was reported at high significance in 2008 by Ho ''et al.''<ref>{{Cite journal |last1=Ho |first1=Shirley |last2=Hirata |last3=Padmanabhan |first3=Nikhil |last4=Seljak |first4=Uros |last5=Bahcall |first5=Neta |year=2008 |title=Correlation of cosmic microwave background with large-scale structure: I. ISW Tomography and Cosmological Implications |journal=Physical Review D |volume=78 |issue=4 |pages=043519 |arxiv=0801.0642 |bibcode=2008PhRvD..78d3519H |doi=10.1103/PhysRevD.78.043519 |s2cid=38383124}}</ref> and Giannantonio ''et al.''<ref>{{Cite journal |last1=Giannantonio |first1=Tommaso |last2=Scranton |first2=Ryan |last3=Crittenden |last4=Nichol |last5=Boughn |last6=Myers |last7=Richards |year=2008 |title=Combined analysis of the integrated Sachs–Wolfe effect and cosmological implications |journal=Physical Review D |volume=77 |issue=12 |pages=123520 |arxiv=0801.4380 |bibcode=2008PhRvD..77l3520G |doi=10.1103/PhysRevD.77.123520 |s2cid=21763795}}</ref>

===Observational Hubble constant data===
A new approach to test evidence of dark energy through observational [[Hubble constant]] data (OHD), also known as cosmic chronometers, has gained significant attention in recent years.<ref>{{cite journal |last1=Yi |first1=Zelong |last2=Zhang |first2=Tongjie |year=2007 |title=Constraints on holographic dark energy models using the differential ages of passively evolving galaxies |journal=[[Modern Physics Letters A]] |volume=22 |issue=1 |pages=41–54 |arxiv=astro-ph/0605596 |bibcode=2007MPLA...22...41Y |doi=10.1142/S0217732307020889 |s2cid=8220261}}</ref><ref>{{Cite journal |last1=Wan |first1=Haoyi |last2=Yi |first2=Zelong |last3=Zhang |first3=Tongjie |last4=Zhou |first4=Jie |year=2007 |title=Constraints on the DGP Universe Using Observational Hubble parameter |journal=Physics Letters B |volume=651 |issue=5 |pages=1368–1379 |arxiv=0706.2723 |bibcode=2007PhLB..651..352W |doi=10.1016/j.physletb.2007.06.053 |s2cid=119125999}}</ref><ref>{{Cite journal |last1=Ma |first1=Cong |last2=Zhang |first2=Tongjie |year=2011 |title=Power of observational Hubble parameter data: a figure of merit exploration |journal=Astrophysical Journal |volume=730 |issue=2 |pages=74 |arxiv=1007.3787 |bibcode=2011ApJ...730...74M |doi=10.1088/0004-637X/730/2/74 |s2cid=119181595}}</ref><ref>{{cite journal |last1=Zhang |first1=Tongjie |last2=Ma |first2=Cong |last3=Lan |first3=Tian |year=2010 |title=Constraints on the dark side of the universe and observational Hubble parameter data |journal=[[Advances in Astronomy]] |volume=2010 |issue=1 |pages=1 |arxiv=1010.1307 |bibcode=2010AdAst2010E..81Z |doi=10.1155/2010/184284 |s2cid=62885316 |doi-access=free}}</ref>

The Hubble constant, ''H''(''z''), is measured as a function of cosmological [[redshift]]. OHD directly tracks the expansion history of the universe by taking passively evolving early-type galaxies as "cosmic chronometers".<ref>{{cite journal |last1=Simon |first1=Joan |last2=Verde |first2=Licia |last3=Jimenez |first3=Raul |year=2005 |title=Constraints on the redshift dependence of the dark energy potential |journal=[[Physical Review D]] |volume=71 |issue=12 |page=123001 |arxiv=astro-ph/0412269 |bibcode=2005PhRvD..71l3001S |doi=10.1103/PhysRevD.71.123001 |s2cid=13215290}}</ref> From this point, this approach provides standard clocks in the universe. The core of this idea is the measurement of the differential age evolution as a function of redshift of these cosmic chronometers. Thus, it provides a direct estimate of the Hubble parameter

:<math> H(z)=-\frac{1}{1+z} \frac{dz}{dt} \approx -\frac{1}{1+z} \frac{\Delta z}{\Delta t}.</math>

The reliance on a differential quantity, {{math|{{sfrac|Δ''z''|Δ''t''}},}} brings more information and is appealing for computation: It can minimize many common issues and systematic effects. Analyses of [[supernova]]e and [[baryon acoustic oscillations]] (BAO) are based on integrals of the Hubble parameter, whereas {{math|{{sfrac|Δ''z''|Δ''t''}} }} measures it directly. For these reasons, this method has been widely used to examine the accelerated cosmic expansion and study properties of dark energy.{{citation needed|date=July 2021}}<!-- Needed citation might be a repeat of one or more of those immediately above -->

==Theories of dark energy==
Dark energy's status as a hypothetical force with unknown properties makes it an active target of research. The problem is attacked from a variety of angles, such as modifying the prevailing theory of gravity (general relativity), attempting to pin down the properties of dark energy, and finding alternative ways to explain the observational data.
[[File:Wz-z.jpg|right|thumb|upright=1.4|The equation of state of Dark Energy for 4 common models by Redshift.<ref>by Ehsan Sadri Astrophysics MSc, Azad University, Tehran</ref> <br />
A: CPL Model, <br />
B: Jassal Model, <br />
C: Barboza & Alcaniz Model,<br />
D: Wetterich Model]]

===Cosmological constant===
{{main|Cosmological constant}}
{{Further|Equation of state (cosmology)}}
[[File:DMPie 2013.svg|thumb|upright=1.4|Estimated distribution of [[matter]] and [[energy]] in the universe<ref name="esa">{{Cite web |title=Planck reveals an almost perfect universe |url=http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe |date=21 March 2013 |website=Planck |publisher=[[ESA]] |access-date=21 March 2013 |archive-date=6 December 2013 |archive-url=https://web.archive.org/web/20131206222557/http://www.esa.int/Our%5FActivities/Space%5FScience/Planck/Planck%5Freveals%5Fan%5Falmost%5Fperfect%5FUniverse |url-status=live }}</ref>]]
The simplest explanation for dark energy is that it is an intrinsic, fundamental energy of space. This is the cosmological constant, usually represented by the Greek letter {{math|Λ}} (Lambda, hence the name [[Lambda-CDM model]]). Since energy and mass are related according to the equation {{nowrap| {{math|''E'' {{=}} ''mc''<sup>2</sup>}},}} Einstein's theory of [[general relativity]] predicts that this energy will have a gravitational effect. It is sometimes called a ''[[vacuum energy]]'' because it is the energy density of empty space – a [[vacuum]].

A major outstanding [[Unsolved problems in physics|problem]] is that the same [[quantum field theory|quantum field theories]] predict a huge [[cosmological constant]], about 120&nbsp;[[orders of magnitude]] too large. This would need to be almost, but not exactly, cancelled by an equally large term of the opposite sign.<ref name=carroll/>

Some [[supersymmetry|supersymmetric]] theories require a cosmological constant that is exactly zero.<ref>{{cite book |last1=Wess |first1=Julius |last2=Bagger |first2=Jonathan |year=1992 |title=Supersymmetry and Supergravity |publisher=Princeton University Press |isbn=978-0691025308}}</ref> Also, it is unknown if there is a metastable vacuum state in [[string theory]] with a positive cosmological constant,<ref name="Wolchover">{{cite magazine |last=Wolchover |first=Natalie |date=9 August 2018 |title=Dark energy may be incompatible with string theory |magazine=[[Quanta Magazine]] |publisher=Simons Foundation |url=https://www.quantamagazine.org/dark-energy-may-be-incompatible-with-string-theory-20180809/ |access-date=2 April 2020 |archive-date=15 November 2020 |archive-url=https://web.archive.org/web/20201115210807/https://www.quantamagazine.org/dark-energy-may-be-incompatible-with-string-theory-20180809/ |url-status=live }}</ref> and it has been conjectured by Ulf Danielsson ''et al.'' that no such state exists.<ref>{{cite journal|last1=Danielsson|first1=Ulf|last2=Van Riet|first2=Thomas|title=What if string theory has no de Sitter vacua?|journal=International Journal of Modern Physics D|date=April 2018|volume=27|issue=12|pages=1830007–1830298|doi=10.1142/S0218271818300070|arxiv=1804.01120|bibcode=2018IJMPD..2730007D|s2cid=119198922|url=https://lirias.kuleuven.be/handle/123456789/626152}}</ref> This conjecture would not rule out other models of dark energy, such as quintessence, that could be compatible with string theory.<ref name="Wolchover" />

===Quintessence===
{{main|Quintessence (physics)}}
In [[quintessence (physics)|quintessence]] models of dark energy, the observed acceleration of the scale factor is caused by the potential energy of a dynamical [[scalar field|field]], referred to as quintessence field. Quintessence differs from the cosmological constant in that it can vary in space and time. In order for it not to clump and form [[large-scale structure of the cosmos|structure]] like matter, the field must be very light so that it has a large [[Compton wavelength]]. In the simplest scenarios, the quintessence field has a canonical kinetic term, is minimally coupled to gravity, and does not feature higher order operations in its Lagrangian.

No evidence of quintessence is yet available, nor has it been ruled out. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some scientists think that the best evidence for quintessence would come from violations of Einstein's [[equivalence principle]] and [[equivalence principle#Tests of the Einstein equivalence principle|variation of the fundamental constants]] in space or time.<ref name="Carroll1998">{{Cite journal |last=Carroll |first=Sean M. |year=1998 |title=Quintessence and the Rest of the World: Suppressing Long-Range Interactions |journal=Physical Review Letters |volume=81 |issue=15 |pages=3067–3070 |arxiv=astro-ph/9806099 |bibcode=1998PhRvL..81.3067C |doi=10.1103/PhysRevLett.81.3067 |s2cid=14539052 |issn=0031-9007}}</ref> [[Scalar field]]s are predicted by the [[Standard Model]] of particle physics and [[string theory]], but an analogous problem to the cosmological constant problem (or the problem of constructing models of [[cosmological inflation]]) occurs: [[renormalization]] theory predicts that scalar fields should acquire large masses.

The coincidence problem asks why the [[accelerating universe|acceleration]] of the Universe began when it did. If acceleration began earlier in the universe, structures such as [[galaxy|galaxies]] would never have had time to form, and life, at least as we know it, would never have had a chance to exist. Proponents of the [[anthropic principle]] view this as support for their arguments. However, many models of quintessence have a so-called "tracker" behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until [[Big Bang|matter–radiation equality]], which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low [[energy scale]] of the dark energy.<ref>{{Cite journal |last1=Ratra |first1=Bharat |last2=Peebles |first2=P. J. E. |year=1988 |title=Cosmological consequences of a rolling homogeneous scalar field |journal=Phys. Rev. |volume=D37 |issue=12 |pages=3406–3427 |bibcode=1988PhRvD..37.3406R |doi=10.1103/PhysRevD.37.3406 |pmid=9958635|doi-access=free }}</ref><ref>{{Cite journal |last1=Steinhardt |first1=Paul J. |last2=Wang |first2=Li-Min |last3=Zlatev |first3=Ivaylo |year=1999 |title=Cosmological tracking solutions |journal=Phys. Rev. |volume=D59 |issue=12 |pages=123504 |arxiv=astro-ph/9812313 |bibcode=1999PhRvD..59l3504S |doi=10.1103/PhysRevD.59.123504|s2cid=40714104 }}</ref>

In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the [[Equation of state (cosmology)|equation of state]] had possibly crossed the cosmological constant boundary (w&nbsp;=&nbsp;−1) from above to below. A [[no-go theorem]] has been proved that this scenario requires models with at least two types of quintessence. This scenario is the so-called [[Quintom scenario]].<ref>{{cite journal |last1=Cai |first1=Yi-Fu |last2=Saridakis |first2=Emmanuel N. |last3=Setare |first3=Mohammed R. |last4=Xia |first4=Jun-Qing |date=22 Apr 2010 |title=Quintom Cosmology – theoretical implications and observations |journal=Physics Reports |volume=493 |issue=1 |pages=1–60 |arxiv=0909.2776 |bibcode=2010PhR...493....1C |doi=10.1016/j.physrep.2010.04.001 |s2cid=118866606}}</ref>

Some special cases of quintessence are [[phantom energy]], in which the energy density of quintessence actually increases with time, and k-essence (short for kinetic quintessence) which has a non-standard form of [[kinetic energy]] such as a [[negative kinetic energy]].<ref>{{Cite journal |last=Caldwell |first=R. R. |date=2002 |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 |arxiv=astro-ph/9908168 |bibcode=2002PhLB..545...23C |doi=10.1016/S0370-2693(02)02589-3 |s2cid=9820570}}</ref> They can have unusual properties: [[phantom energy]], for example, can cause a [[Big Rip]].

A group of researchers argued in 2021 that observations of the [[Hubble tension]] may imply that only quintessence models with a nonzero [[coupling constant]] are viable.<ref name="FLRW breakdown">{{cite journal |last1=Krishnan |first1=Chethan |last2=Mohayaee |first2=Roya |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Does Hubble Tension Signal a Breakdown in FLRW Cosmology? |journal=Classical and Quantum Gravity |date=16 September 2021 |volume=38 |issue=18 |pages=184001 |doi=10.1088/1361-6382/ac1a81 |arxiv=2105.09790 |bibcode=2021CQGra..38r4001K |s2cid=234790314 |issn=0264-9381}}</ref>

===Interacting dark energy===
This class of theories attempts to come up with an all-encompassing theory of both dark matter and dark energy as a single phenomenon that modifies the laws of gravity at various scales. This could, for example, treat dark energy and dark matter as different facets of the same unknown substance,<ref>See [[dark fluid]].</ref> or postulate that cold dark matter decays into dark energy.<ref>{{Cite arXiv |eprint=1610.01272 |class=astro-ph.CO |first=Rafael J. F. |last=Marcondes |title=Interacting dark energy models in Cosmology and large-scale structure observational tests |date=5 October 2016}}</ref> Another class of theories that unifies dark matter and dark energy are suggested to be covariant theories of modified gravities. These theories alter the dynamics of spacetime such that the modified dynamics stems to what have been assigned to the presence of dark energy and dark matter.<ref>{{Cite journal |last=Exirifard |first=Q. |year=2011 |title=Phenomenological covariant approach to gravity |journal=General Relativity and Gravitation |volume=43 |issue=1 |pages=93–106 |arxiv=0808.1962 |bibcode=2011GReGr..43...93E |doi=10.1007/s10714-010-1073-6|s2cid=119169726 }}</ref> Dark energy could in principle interact not only with the rest of the dark sector, but also with ordinary matter. However, cosmology alone is not sufficient to effectively constrain the strength of the coupling between dark energy and baryons, so that other indirect techniques or laboratory searches have to be adopted.<ref>{{Cite journal |last1=Vagnozzi |first1=Sunny |last2=Visinelli |first2=Luca |last3=Mena |first3=Olga |last4=Mota |first4=David F. |year=2020 |title=Do we have any hope of detecting scattering between dark energy and baryons through cosmology? |journal=Monthly Notices of the Royal Astronomical Society |volume=493 |issue=1 |pages=1139–1152 |arxiv=1911.12374 |bibcode=2020MNRAS.493.1139V |doi=10.1093/mnras/staa311}}</ref> It was briefly theorized in the early 2020s that excess observed in the [[XENON|XENON1T]] detector in Italy may have been caused by a [[chameleon particle|chameleon]] model of dark energy, but further experiments disproved this possibility.<ref>{{Cite web |date=2022-07-22 |title=A new dark matter experiment quashed earlier hints of new particles |url=https://www.sciencenews.org/article/xenonnt-axions-dark-matter-experiment |access-date=2022-08-03 |website=Science News |language=en-US |archive-date=26 August 2022 |archive-url=https://web.archive.org/web/20220826064807/https://www.sciencenews.org/article/xenonnt-axions-dark-matter-experiment |url-status=live }}</ref><ref>{{cite journal |last1=Aprile |first1=E. |last2=Abe |first2=K. |last3=Agostini |first3=F. |last4=Maouloud |first4=S. Ahmed |last5=Althueser |first5=L. |last6=Andrieu |first6=B. |last7=Angelino |first7=E. |last8=Angevaare |first8=J. R. |last9=Antochi |first9=V. C. |last10=Martin |first10=D. Antón |last11=Arneodo |first11=F. |date=2022-07-22 |title=Search for New Physics in Electronic Recoil Data from XENONnT |journal=Physical Review Letters |volume=129 |issue=16 |page=161805 |doi=10.1103/PhysRevLett.129.161805 |pmid=36306777 |arxiv=2207.11330 |bibcode=2022PhRvL.129p1805A |s2cid=251040527 }}</ref>

===Variable dark energy models===
The density of dark energy might have varied in time during the history of the universe. Modern observational data allows us to estimate the present density of dark energy. Using [[baryon acoustic oscillations]], it is possible to investigate the effect of dark energy in the history of the Universe, and constrain parameters of the [[equation of state]] of dark energy. To that end, several models have been proposed. One of the most popular models is the Chevallier–Polarski–Linder model (CPL).<ref>{{Cite journal |last1=Chevallier |first1=M |last2=Polarski |first2=D |year=2001 |title=Accelerating Universes with Scaling Dark Matter |journal=International Journal of Modern Physics D |volume=10 |issue=2 |pages=213–224 |arxiv=gr-qc/0009008 |bibcode=2001IJMPD..10..213C |doi=10.1142/S0218271801000822|s2cid=16489484 }}</ref><ref>{{Cite journal |last=Linder |first=Eric V. |date=3 March 2003 |title=Exploring the Expansion History of the Universe |journal=Physical Review Letters |volume=90 |issue=9 |page=091301 |arxiv=astro-ph/0208512 |bibcode=2003PhRvL..90i1301L |doi=10.1103/PhysRevLett.90.091301 |pmid=12689209|s2cid=16219710 }}</ref> Some other common models are (Barboza & Alcaniz. 2008),<ref>{{Cite journal |last1=Barboza|first1=E.M. |last2=Alcaniz |first2=J.S. |year=2008 |title=A parametric model for dark energy |journal=Physics Letters B |volume=666 |issue=5 |pages=415–419 |arxiv=0805.1713 |bibcode=2008PhLB..666..415B |doi=10.1016/j.physletb.2008.08.012|s2cid=118306372 }}</ref> (Jassal et al. 2005),<ref>{{Cite journal |last1=Jassal |first1=H.K |last2=Bagla |first2=J.S |year=2010 |title=Understanding the origin of CMB constraints on Dark Energy |journal=Monthly Notices of the Royal Astronomical Society |volume=405 |issue=4 |pages=2639–2650 |arxiv=astro-ph/0601389 |bibcode=2010MNRAS.405.2639J |doi=10.1111/j.1365-2966.2010.16647.x|s2cid=9144993 }}</ref> (Wetterich. 2004),<ref>{{Cite journal |last=Wetterich |first=C. |date=2004 |title=Phenomenological parameterization of quintessence |journal=Physics Letters B |volume=594 |issue=1–2 |pages=17–22 |arxiv=astro-ph/0403289 |bibcode=2004PhLB..594...17W |doi=10.1016/j.physletb.2004.05.008|s2cid=119354763 }}</ref> and (Oztas et al. 2018).<ref>{{Cite journal |last1=Oztas |first1=A. |last2=Dil |first2=E. |last3=Smith |first3=M.L. |date=2018 |title=The varying cosmological constant: a new approximation to the Friedmann equations and universe model |journal=Mon. Not. R. Astron. Soc. |volume=476 |issue=1 |pages=451–458 |bibcode=2018MNRAS.476..451O |doi=10.1093/mnras/sty221}}</ref><ref>{{Cite journal |last=Oztas |first=A. |date=2018 |title=The effects of a varying cosmological constant on the particle horizon |journal=Mon. Not. R. Astron. Soc. |volume=481 |issue=2 |pages=2228–2234 |bibcode=2018MNRAS.481.2228O |doi=10.1093/mnras/sty2375}}</ref>

===Observational skepticism===
Some alternatives to dark energy, such as [[inhomogeneous cosmology]], aim to explain the observational data by a more refined use of established theories. In this scenario, dark energy does not actually exist, and is merely a measurement artifact. 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. |year=2007 |title=Exact Solution to the Averaging Problem in Cosmology |journal=Physical Review Letters |volume=99 |issue=25 |page=251101 |arxiv=0709.0732 |bibcode=2007PhRvL..99y1101W |doi=10.1103/PhysRevLett.99.251101 |pmid=18233512|s2cid=1152275 }}</ref><ref>{{Cite journal |last1=Ishak, Mustapha |last2=Richardson, James |last3=Garred, David |last4=Whittington, Delilah |last5=Nwankwo, Anthony |last6=Sussman, Roberto |year=2008 |title=Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW? |journal=Physical Review D |volume=78 |issue=12 |pages=123531 |arxiv=0708.2943 |bibcode=2008PhRvD..78l3531I |doi=10.1103/PhysRevD.78.123531|s2cid=118801032 }}</ref><ref>{{Cite journal |last=Mattsson, Teppo |year=2010 |title=Dark energy as a mirage |journal=Gen. Rel. Grav. |volume=42 |issue=3 |pages=567–599 |arxiv=0711.4264 |bibcode=2010GReGr..42..567M |doi=10.1007/s10714-009-0873-z|s2cid=14226736 }}</ref><ref>{{Cite journal |last1=Clifton |first1=Timothy |last2=Ferreira, Pedro |date=April 2009 |title=Does Dark Energy Really Exist? |journal=Scientific American |volume=300 |issue=4 |pages=48–55 |bibcode=2009SciAm.300d..48C |doi=10.1038/scientificamerican0409-48 |pmid=19363920}}</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 |last=Wiltshire |first=D. |year=2008 |title=Cosmological equivalence principle and the weak-field limit |journal=Physical Review D |volume=78 |issue=8 |pages=084032 |arxiv=0809.1183 |bibcode=2008PhRvD..78h4032W |doi=10.1103/PhysRevD.78.084032|s2cid=53709630 }}</ref><ref>{{Cite web |title=Dark questions remain over dark energy |url=http://www.abc.net.au/science/articles/2009/12/09/2765371.htm |last=Gray |first=Stuart |date=8 December 2009 |publisher=ABC Science Australia |access-date=27 January 2013 |archive-date=15 January 2013 |archive-url=https://web.archive.org/web/20130115080629/http://www.abc.net.au/science/articles/2009/12/09/2765371.htm |url-status=live }}</ref><ref>{{Cite news |last=Merali |first=Zeeya |date=March 2012 |title=Is Einstein's Greatest Work All Wrong – Because He Didn't Go Far Enough? |work=Discover magazine |url=http://discovermagazine.com/2012/mar/09-is-einsteins-greatest-work-wrong-didnt-go-far |access-date=27 January 2013 |archive-date=28 January 2013 |archive-url=https://web.archive.org/web/20130128075325/http://discovermagazine.com/2012/mar/09-is-einsteins-greatest-work-wrong-didnt-go-far |url-status=live }}</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) [http://www.nbcnews.com/id/44690771 'Accelerating universe' could be just an illusion] {{Webarchive|url=https://web.archive.org/web/20200924002445/http://www.nbcnews.com/id/44690771 |date=24 September 2020 }}, NBC News</ref><ref>{{Cite journal |last=Tsagas |first=Christos G. |year=2011 |title=Peculiar motions, accelerated expansion, and the cosmological axis |journal=Physical Review D |volume=84 |issue=6 |pages=063503 |arxiv=1107.4045 |bibcode=2011PhRvD..84f3503T |doi=10.1103/PhysRevD.84.063503|s2cid=119179171 }}</ref> or that the statistical methods employed were flawed.<ref name="sarkar">{{Cite journal |last1=Nielsen |first1=J. T. |last2=Guffanti |first2=A. |last3=Sarkar |first3=S. |date=21 October 2016 |title=Marginal evidence for cosmic acceleration from Type Ia supernovae |journal=Scientific Reports |volume=6 |page=35596 |arxiv=1506.01354 |bibcode=2016NatSR...635596N |doi=10.1038/srep35596 |pmc=5073293 |pmid=27767125}}</ref><ref name="ox.ac.uk">{{Cite web |last=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-%E2%80%93-or-it |url-status=live |archive-url=https://web.archive.org/web/20170726092531/http://www.ox.ac.uk/news/science-blog/universe-expanding-accelerating-rate-%E2%80%93-or-it |archive-date=26 July 2017 |access-date=10 August 2017 |website=University of Oxford – News & Events – Science Blog ([[WP:NEWSBLOG]])}}</ref> A laboratory direct detection attempt failed to detect any force associated with dark energy.<ref name="Sabulsky">{{Cite journal |last1=Sabulsky |first1=D. O. |last2=Dutta |first2=I. |last3=Hinds |first3=E. A. |last4=Elder |first4=B. |last5=Burrage |first5=C. |last6=Copeland |first6=E. J. |year=2019 |title=Experiment to Detect Dark Energy Forces Using Atom Interferometry |journal=Physical Review Letters |volume=123 |issue=6 |pages=061102 |arxiv=1812.08244 |bibcode=2019PhRvL.123f1102S |doi=10.1103/PhysRevLett.123.061102 |pmid=31491160 |s2cid=118935116}}</ref>

Observational skepticism explanations of dark energy have generally not gained much traction among cosmologists. For example, a paper that suggested the anisotropy of the local Universe has been misrepresented as dark energy<ref>{{Cite journal |last1=Colin|first1=Jacques |last2=Mohayaee|first2=Roya|last3=Rameez|first3=Mohamed|last4=Sakar|first4=Subir|date=22 July 2019|title=Evidence for anisotropy of cosmic acceleration|journal=Astronomy & Astrophysics|volume=631|pages=L13 |arxiv=1808.04597|doi=10.1051/0004-6361/201936373|bibcode=2019A&A...631L..13C |s2cid=208175643 }}</ref> was quickly countered by another paper claiming errors in the original paper.<ref>{{Cite journal |last1=Rubin |first1=D. |last2=Heitlauf |first2=J. |date=6 May 2020 |title=Is the Expansion of the Universe Accelerating? All Signs Still Point to Yes: A Local Dipole Anisotropy Cannot Explain Dark Energy |journal=The Astrophysical Journal |volume=894 |issue=1 |pages=68 |arxiv=1912.02191 |doi=10.3847/1538-4357/ab7a16 |bibcode=2020ApJ...894...68R |s2cid=208637339 |issn=1538-4357 |doi-access=free }}</ref> Another study questioning the essential assumption that the luminosity of Type Ia supernovae does not vary with stellar population age<ref name="PHYS-20200106">{{Cite news |last=Yonsei University |author-link=Yonsei University |date=6 January 2020 |title=New evidence shows that the key assumption made in the discovery of dark energy is in error |work=[[Phys.org]] |url=https://phys.org/news/2020-01-evidence-key-assumption-discovery-dark.html |access-date=6 January 2020 |archive-date=13 January 2020 |archive-url=https://web.archive.org/web/20200113024133/https://phys.org/news/2020-01-evidence-key-assumption-discovery-dark.html |url-status=live }}</ref><ref name="ARX-20191210">{{Cite journal |last=Kang |first=Yijung |display-authors=et al. |year=2020 |title=Early-type Host Galaxies of Type Ia Supernovae. II. Evidence for Luminosity Evolution in Supernova Cosmology |journal=The Astrophysical Journal |volume=889 |issue=1 |pages=8 |arxiv=1912.04903 |bibcode=2020ApJ...889....8K |doi=10.3847/1538-4357/ab5afc|s2cid=209202868 |doi-access=free }}</ref> was also swiftly rebutted by other cosmologists.<ref>{{Cite web |last=Gohd |first=Chelsea |date=9 January 2020 |title=Has Dark Energy Been Debunked? Probably Not. |url=https://www.space.com/dark-energy-not-debunked.html |url-status=live |archive-url=https://web.archive.org/web/20200302053942/https://www.space.com/dark-energy-not-debunked.html |archive-date=2 March 2020 |access-date=14 February 2020 |website=Space.com |language=en-us}}</ref>

===As a general relativistic effect due to black holes===
This theory was formulated by [[University of Hawaiʻi at Mānoa]] researchers in February 2023. The idea is that if one requires the [[Kerr metric]] (which describes rotating black holes) to asymptote to the [[Friedmann-Robertson-Walker metric]] (which describes the [[isotropic]] and [[homogeneous]] universe that is the basic assumption of modern cosmology), then one finds that black holes gain mass as the universe expands. The rate is measured to be {{math|∝''a''<sup>3</sup>}}, where ''a'' is the [[scale factor]]. This particular rate means that the energy density of black holes remain constant over time, mimicking dark energy (see [[Dark_energy#Technical_definition]]). The theory is called "cosmological coupling" because the black holes couple to a cosmological requirement.<ref>{{Cite web |title=Wait... Did We Finally Find the Source of Dark Energy?! |url=https://www.msn.com/en-us/news/technology/wait-did-we-finally-find-the-source-of-dark-energy/ar-AA17zXBB |access-date=2023-04-04 |website=MSN |language=en-US}}</ref> Other astrophysicists are skeptical,<ref>{{cite web |author=Siegel |first=Ethan |author-link=Ethan Siegel |date=17 February 2023 |title=Ask Ethan: Can black holes really cause dark energy? |url=https://bigthink.com/starts-with-a-bang/black-holes-dark-energy/ |publisher=Starts with a Bang}}</ref> with a variety of papers claiming that the theory fails to explain other observations.<ref>{{cite web |author=Rodriguez |first=Carl L. |title=No, black holes are not the source of dark energy |url=https://dynamics.unc.edu/2023/03/02/no-black-holes-are-not-the-source-of-dark-energy/ |accessdate=11 September 2023}}</ref><ref>{{cite journal |author=Ghodla |first1=Sohan |last2=Easther |first2=Richard |last3=Briel |first3=M. M. |last4=Eldridge |first4=J. J. |date=20 July 2023 |title=Observational implications of cosmologically coupled black holes |journal=The Open Journal of Astrophysics |volume=6 |page=25 |doi=10.21105/astro.2306.08199 |arxiv=2306.08199 |bibcode=2023OJAp....6E..25G |s2cid=259165172 }}</ref>

==Other mechanism driving acceleration==
===Modified gravity===
{{see also|Massive gravity}}
The evidence for dark energy is heavily dependent on the theory of general relativity. Therefore, it is conceivable that a [[Alternatives to general relativity|modification to general relativity]] also eliminates the need for dark energy. There are many such theories, and research is ongoing.<ref>See {{Cite journal |last1=Sami |first1=M. |last2=Myrzakulov |first2=R. |year=2015 |title=Late time cosmic acceleration: ABCD of dark energy and modified theories of gravity |journal=International Journal of Modern Physics D |volume=25 |issue=12 |pages=1630031 |arxiv=1309.4188 |bibcode=2016IJMPD..2530031S |doi=10.1142/S0218271816300317 |s2cid=119256879}} for a recent review</ref><ref>{{Cite journal |last1=Joyce |first1=Austin |last2=Lombriser |first2=Lucas |last3=Schmidt |first3=Fabian |year=2016 |title=Dark Energy vs. Modified Gravity |journal=[[Annual Review of Nuclear and Particle Science]] |volume=66 |issue=1 |pages=95 |arxiv=1601.06133 |bibcode=2016ARNPS..66...95J |doi=10.1146/annurev-nucl-102115-044553 |s2cid=118468001 |doi-access=free}}</ref> The measurement of the speed of gravity in the first gravitational wave measured by non-gravitational means ([[GW170817]]) ruled out many modified gravity theories as explanations to dark energy.<ref>{{Cite journal |last1=Lombriser |first1=Lucas |last2=Lima |first2=Nelson |year=2017 |title=Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure |journal=Physics Letters B |volume=765 |pages=382–385 |arxiv=1602.07670 |bibcode=2017PhLB..765..382L |doi=10.1016/j.physletb.2016.12.048|s2cid=118486016 }}</ref><ref>{{Cite news |date=10 February 2017 |title=Quest to settle riddle over Einstein's theory may soon be over |work=[[phys.org]] |url=https://phys.org/news/2017-02-quest-riddle-einstein-theory.html |access-date=29 October 2017 |archive-date=28 October 2017 |archive-url=https://web.archive.org/web/20171028042919/https://phys.org/news/2017-02-quest-riddle-einstein-theory.html |url-status=live }}</ref><ref>{{Cite news |date=25 February 2017 |title=Theoretical battle: Dark energy vs. modified gravity |work=[[Ars Technica]] |url=https://arstechnica.co.uk/science/2017/02/theoretical-battle-dark-energy-vs-modified-gravity/ |access-date=27 October 2017 |archive-date=28 October 2017 |archive-url=https://web.archive.org/web/20171028042608/https://arstechnica.co.uk/science/2017/02/theoretical-battle-dark-energy-vs-modified-gravity/ |url-status=live }}</ref>

Astrophysicist [[Ethan Siegel]] states that, while such alternatives gain mainstream press coverage, almost all professional astrophysicists are confident that dark energy exists and that none of the competing theories successfully explain observations to the same level of precision as standard dark energy.<ref>{{Cite news |last=Siegel |first=Ethan |date=2018 |title=What Astronomers Wish Everyone Knew About Dark Matter And Dark Energy |language=en |work=Forbes (Starts With A Bang blog) |url=https://www.forbes.com/sites/startswithabang/2018/04/10/what-astronomers-wish-everyone-knew-about-dark-matter-and-dark-energy/ |access-date=11 April 2018 |archive-date=11 April 2018 |archive-url=https://web.archive.org/web/20180411124424/https://www.forbes.com/sites/startswithabang/2018/04/10/what-astronomers-wish-everyone-knew-about-dark-matter-and-dark-energy/ |url-status=live }}</ref>

===Non-linearities of General Relativity equations===
The [[Non-standard_cosmology#GRSI model|GRSI model]] explains the [[accelerating expansion of the universe]] a suppression of gravity as large distance.<ref name="Deur19a">{{cite journal |arxiv=1709.02481|doi=10.1140/epjc/s10052-019-7393-0|title=An explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity|year=2019|last1=Deur|first1=Alexandre|journal=Eur. Phys. Jour. C|issue=79|page=883}}</ref> Such suppression is a consequence of an increased [[binding energy]] within a galaxy due to General Relativity's field self-interaction. The increased binding requires, by [[energy conservation]], a suppression of gravitational attraction outside said galaxy. The suppression is in lieu of dark energy. This is analogous to the central phenomenology of [[Strong interaction|Strong Nuclear Force]] where the [[gluons]] field self-interaction dramatically strengthens the binding of quarks, ultimately leading to their [[Color confinement|confinement]]. This in turn [[Nuclear force|suppresses the Strong Nuclear Force outside hadrons]].

==Implications for the fate of the universe==
Cosmologists estimate that the [[Deceleration parameter|acceleration]] began 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 |date=1 January 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|s2cid=15117520 }}</ref>{{efn|1=
Taken from Frieman, Turner, & Huterer (2008):<ref name=Frieman/>{{rp|pages=6, 44}}<br/>
"The Universe has gone through three distinct eras:
: Radiation-dominated, {{nowrap|&nbsp; {{math| ''z'' ≳ 3000}} ;}}
: Matter-dominated, {{nowrap|&nbsp; {{math| 3000 ≳ ''z'' ≳ 0.5}} ;}} and
: Dark-energy-dominated, {{nowrap|&nbsp; {{math| 0.5 ≳ ''z''}} .}}
The evolution of the scale factor is controlled by the dominant energy form:
::<math>\; a(t) \propto t^{\frac{2}{3} (1 + w)^{-1}} ~</math>
(for constant &nbsp;{{mvar|w}}&nbsp;).
During the radiation-dominated era,
:: <math>\; a(t) \propto t^{1/2} ~</math>
during the matter-dominated era,
:: <math>\; a(t) \propto t^{2/3} ~</math>
and for the dark energy-dominated era, assuming {{nowrap|&nbsp; {{math|''w'' ≃ −1}} &nbsp;}} asymptotically 
:: <math>\; a(t) \propto e^{H\,t} ~.</math><ref name=Frieman/>{{rp|page=6}}

"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, {{nowrap| 0.76 ± 0.02 ,}} and the equation-of-state parameter:
::{{nowrap|&nbsp; {{math|''w'' ≈ −1 ± 0.1}} {{grey|{{small|[stat.]}} }} {{math|± 0.1}} {{grey|{{small|[sys.]}} }} ,}}
assuming that &nbsp;{{mvar|w}}&nbsp; is constant. This implies that the Universe began accelerating at redshift {{nowrap|&nbsp; {{math|''z'' ~}} 0.4 &nbsp;}} and age {{nowrap|&nbsp; {{math|''t'' ~}} 10 [[Gigaannum|Ga]] .}} 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."<ref name=Frieman/>{{rp|page=44}}
}} Before that, it is thought that the expansion was decelerating, due to the attractive influence of matter. The density of dark matter in an expanding universe decreases more quickly than dark energy, and eventually the dark energy dominates. Specifically, when the volume of the universe doubles, the density of [[dark matter]] is halved, but the density of dark energy is nearly unchanged (it is exactly constant in the case of a cosmological constant).

Projections into the future can differ radically for different models of dark energy. For a cosmological constant, or any other model that predicts that the acceleration will continue indefinitely, the ultimate result will be that galaxies outside the [[Local Group]] will have a [[radial velocity|line-of-sight velocity]] that continually increases with time, eventually far exceeding the speed of light.<ref>{{cite journal |last1=Krauss, Lawrence M. |last2=Scherrer, Robert J. |date=March 2008 |title=The End of Cosmology? |url=http://www.scientificamerican.com/article.cfm?id=the-end-of-cosmology |journal=Scientific American |volume=82 |access-date=6 January 2011 |archive-date=19 March 2011 |archive-url=https://web.archive.org/web/20110319075823/https://www.scientificamerican.com/article.cfm?id=the-end-of-cosmology |url-status=live }}</ref> This is not a violation of [[special relativity]] because the notion of "velocity" used here is different from that of velocity in a local [[inertial frame of reference]], which is still constrained to be less than the speed of light for any massive object (see [[Comoving and proper distances#Uses of the proper distance|Uses of the proper distance]] for a discussion of the subtleties of defining any notion of relative velocity in cosmology). Because the [[Hubble's law#Interpretation|Hubble parameter]] is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.<ref>[http://curious.astro.cornell.edu/question.php?number=575 Is the universe expanding faster than the speed of light?] {{webarchive|url=https://web.archive.org/web/20031123150109/http://curious.astro.cornell.edu/question.php?number=575 |date=23 November 2003 }} (see the last two paragraphs)</ref><ref name="ly93">{{Cite web |last1=Lineweaver |first1=Charles |last2=Davis |first2=Tamara M. |year=2005 |title=Misconceptions about the Big Bang |url=http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf |archive-url=https://web.archive.org/web/20110719235653/http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf |archive-date=19 July 2011 |access-date=6 November 2008 |website=Scientific American}}</ref>

However, because of the accelerating expansion, it is projected that most galaxies will eventually cross a type of cosmological [[event horizon]] where any light they emit past that point will never be able to reach us at any time in the infinite future<ref>{{Cite journal |last=Loeb |first=Abraham |year=2002 |title=The Long-Term Future of Extragalactic Astronomy |journal=Physical Review D |volume=65 |issue=4 |pages=047301 |arxiv=astro-ph/0107568 |bibcode=2002PhRvD..65d7301L |doi=10.1103/PhysRevD.65.047301|s2cid=1791226 }}</ref> because the light never reaches a point where its "peculiar velocity" toward us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in [[Comoving and proper distances#Uses of the proper distance|Uses of the proper distance]]). Assuming the dark energy is constant (a [[cosmological constant]]), the current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening ''at present'' would eventually be able to reach us in the future if the event were less than 16 billion light years away, but the signal would never reach us if the event were more than 16 billion light years away.<ref name=ly93 />

As galaxies approach the point of crossing this cosmological event horizon, the light from them will become more and more [[redshift]]ed, to the point where the wavelength becomes too large to detect in practice and the galaxies appear to vanish completely<ref>{{Cite journal |last1=Krauss |first1=Lawrence M. |last2=Scherrer |first2=Robert J. |year=2007 |title=The Return of a Static Universe and the End of Cosmology |journal=General Relativity and Gravitation |volume=39 |issue=10 |pages=1545–1550 |arxiv=0704.0221 |bibcode=2007GReGr..39.1545K |doi=10.1007/s10714-007-0472-9 |s2cid=123442313}}</ref><ref>[https://www.npr.org/templates/story/story.php?storyId=102715275 Using Tiny Particles To Answer Giant Questions] {{Webarchive|url=https://web.archive.org/web/20180506104005/https://www.npr.org/templates/story/story.php?storyId=102715275 |date=6 May 2018 }}. Science Friday, 3 April 2009. According to the [https://www.npr.org/templates/transcript/transcript.php?storyId=102715275 transcript] {{Webarchive|url=https://web.archive.org/web/20180506035942/https://www.npr.org/templates/transcript/transcript.php?storyId=102715275 |date=6 May 2018 }}, [[Brian Greene]] makes the comment "And actually, in the far future, everything we now see, except for our local galaxy and a region of galaxies will have disappeared. The entire universe will disappear before our very eyes, and it's one of my arguments for actually funding cosmology. We've got to do it while we have a chance."</ref> (''see'' [[Future of an expanding universe]]). Planet Earth, the [[Milky Way]], and the [[Local Group]] of galaxies of which the Milky Way is a part, would all remain virtually undisturbed as the rest of the universe recedes and disappears from view. In this scenario, the Local Group would ultimately suffer [[heat death of the universe|heat death]], just as was hypothesized for the flat, matter-dominated universe before measurements of [[accelerating expansion of the universe|cosmic acceleration]].{{citation needed|date=June 2022}}

There are other, more speculative ideas about the future of the universe. The [[phantom energy]] model of dark energy results in ''divergent'' expansion, which would imply that the effective force of dark energy continues growing until it dominates all other forces in the universe. Under this scenario, dark energy would ultimately tear apart all gravitationally bound structures, including galaxies and solar systems, and eventually overcome the [[electric force|electrical]] and [[nuclear force]]s to tear apart atoms themselves, ending the universe in a "[[Big Rip]]". On the other hand, dark energy might dissipate with time or even become attractive. Such uncertainties leave open the possibility of gravity eventually prevailing and lead to a universe that contracts in on itself in a "[[Big Crunch]]",<ref name="HTUW">{{Cite AV media |title=How the Universe Works 3 |publisher=Discovery Channel |year=2014 |volume=End of the Universe}}</ref> or that there may even be a dark energy cycle, which implies a [[cyclic model|cyclic model of the universe]] in which every iteration ([[Big Bang]] then eventually a [[Big Crunch]]) takes about a [[1000000000000 (number)|trillion]] (10<sup>12</sup>) years.<ref>{{Cite web |title='Cyclic universe' can explain cosmological constant |url=https://www.newscientist.com/article/dn9114-cyclic-universe-can-explain-cosmological-constant/ |access-date=2023-09-18 |website=New Scientist |language=en-US}}</ref><ref name="Steinhardt & Turok 2002">{{Cite journal |last1=Steinhardt |first1=P. J. |author-link=Paul Steinhardt |last2=Turok, N. |author-link2=Neil Turok |date=25 April 2002 |title=A Cyclic Model of the Universe |journal=[[Science (journal)|Science]] |volume=296 |issue=5572 |pages=1436–1439 |arxiv=hep-th/0111030 |bibcode=2002Sci...296.1436S |doi=10.1126/science.1070462 |pmid=11976408|s2cid=1346107 }}</ref> While none of these are supported by observations, they are not ruled out.{{citation needed|date=June 2022}}

==In philosophy of science==
The astrophysicist [[David Merritt]] identifies dark energy as an example of an "auxiliary hypothesis", an [[Ad hoc hypothesis|ad hoc]] postulate that is added to a theory in response to observations that [[falsifiability|falsify]] it. He argues that the dark energy hypothesis is a [[conventionalism#Epistemology|conventionalist]] hypothesis, that is, a hypothesis that adds no empirical content and hence is [[Falsifiability|unfalsifiable]] in the sense defined by [[Karl Popper]].<ref>{{Cite journal |last=Merritt |first=David |year=2017 |title=Cosmology and convention |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |volume=57 |pages=41–52 |arxiv=1703.02389 |bibcode=2017SHPMP..57...41M |doi=10.1016/j.shpsb.2016.12.002|s2cid=119401938 }}</ref> However, his opinion does not seem to be consensus{{by whom|date=January 2023}} and is at odds with the history of cosmology.{{why|date=January 2023}}<ref>{{Cite journal | last=Helbig | first=Phillip | year=2020 |title=Sonne und Mond, or, the good, the bad, and the ugly: comments on the debate between MOND and LambdaCDM| journal=The Observatory | volume=140 | pages=225–247 | bibcode= 2020Obs...140..225H }}</ref>

==See also==
{{div col|colwidth=20em}}
* [[Conformal gravity]]
* [[Dark Energy Spectroscopic Instrument]]
* [[Dark matter]]
* [[De Sitter invariant special relativity]]
* [[Illustris project]]
* [[Inhomogeneous cosmology]]
* [[Joint Dark Energy Mission]]
* [[Negative mass]]
* ''[[Quintessence: The Search for Missing Mass in the Universe]]''
* ''[[Dark Energy Survey]]''
* [[Quantum vacuum state]]
{{div col end}}

==Notes==
{{notelist}}

==References==
{{reflist}}

==External links==
* [http://sci.esa.int/euclid/ Euclid ESA Satellite], a mission to map the geometry of the dark universe
* [https://arxiv.org/abs/astro-ph/0607066 "Surveying the dark side"]


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