Accelerating expansion of the universe#Supernova observation

{{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,{{cite journal |last1=Penzias |first1=A. A. |last2=Wilson |first2=R. W. |date=1965 |title=A Measurement of Excess Antenna Temperature at 4080 Mc/s |journal=The Astrophysical Journal |volume=142 |issue=1 |pages=419–421 |bibcode=1965ApJ...142..419P |doi=10.1086/148307|doi-access=free }} the Big Bang model has become the most accepted model explaining the evolution of our universe. The Friedmann equation defines how the energy in the universe drives its expansion.

$$H^2=\{\backslash left\; (\; \backslash frac\{\backslash dot\{a\}\}\{a\}\; \backslash right\; )\}^2=\backslash frac\{8\{\backslash pi\}G\}\{3\}\backslash rho-\backslash frac\{\{\backslash kappa\}c^2\}\{a^2\}$$

where {{mvar|κ}} represents the curvature of the universe, {{math|a(t)}} is the scale factor, {{mvar|ρ}} is the total energy density of the universe, and {{mvar|H}} is the Hubble parameter.{{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}}

The critical density is defined as

$$\backslash rho\_c=\backslash frac\{3H^2\}\{8\{\backslash pi\}G\}$$

and the density parameter

$$\backslash Omega=\backslash frac\{\backslash rho\}\{\backslash rho\_c\}$$

The Hubble parameter can then be rewritten as

$$H(a)=H\_0\; \backslash sqrt\{\{\backslash Omega\_ka^\{-2\}\; +\; \backslash Omega\}\_ma^\{-3\}\; +\; \backslash Omega\_ra^\{-4\}\; +\; \backslash Omega\_\backslash mathrm\{DE\}a^\{-3(1+w)\}\}$$

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

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

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

where the pressure {{mvar|P}} is defined by the cosmological model chosen. (see 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|q₀}}.{{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}} Recent observations indicate this deceleration parameter is negative.

According to the theory of 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.

The definition of "accelerating expansion" is that the second time derivative of the cosmic scale factor, $\backslash ddot\{a\}$, is positive, which is equivalent to the deceleration parameter, $q$, being negative. However, note this does not imply that the Hubble parameter is increasing with time. Since the Hubble parameter is defined as $H(t)\; \backslash equiv\; \backslash dot\{a\}(t)\; /\; a(t)$, it follows from the definitions that the derivative of the Hubble parameter is given by

$$\backslash frac\{dH\}\{dt\}\; =\; -H^2(1\; +\; q)$$

so the Hubble parameter is decreasing with time unless . Observations prefer $q\; \backslash approx\; -0.55$, which implies that $\backslash ddot\{a\}$ is positive but $dH/dt$ 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 $a(t)$ is a linear function of $t$, $q\; =\; 0$, $\backslash dot\{a\}\; =\; const$, and $H(t)\; =\; 1/t$.

The rate of expansion of the universe can be analyzed using the magnitude-redshift relationship of astronomical objects using standard candles, or their distance-redshift relationship using standard rulers. Also a factor is the growth of large-scale structure, finding that the observed values of the cosmological parameters are best described by models which include an accelerating expansion.

File:Asymmetric Ashes (artist's impression).jpg

In 1998, the first evidence for acceleration came from the observation of Type Ia supernovae, which are exploding white dwarf stars that have exceeded their 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).{{cite arXiv |last1=Albrecht|first1=Andreas |display-authors=etal |title=Report of the Dark Energy Task Force |date=2006 |eprint=astro-ph/0609591}} Spectral lines of their light can be used to determine their redshift.

For supernovae at redshift less than around 0.1, or light travel time less than 10 percent of the age of the universe, this gives a nearly linear distance–redshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time. The full calculation requires 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.

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

So a supernova with a measured redshift {{math|z {{=}} 0.5}} implies the universe was {{sfrac|1|1 + 0.5}} = {{sfrac|2|3}} of its present size when the supernova exploded. In the case of accelerated expansion, $\backslash ddot\{a\}$ is positive; therefore, $\backslash dot\{a\}$ 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 $\backslash dot\{a\}$ 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_M {{=}} 0.2}} universe without a cosmological constant".{{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 }} This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.{{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}}

Several researchers have questioned the majority opinion on the acceleration or the assumption of the "cosmological principle" (that the universe is homogeneous and isotropic).{{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}} 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.{{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}}{{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}} See also the section on Alternate theories below.

{{Main|Baryon acoustic oscillations}}

In the early universe before recombination and decoupling took place, photons and matter existed in a primordial plasma. Points of higher density in the photon-baryon plasma would contract, being compressed by gravity until the pressure became too large and they expanded again. 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,{{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 }} photons separated from matter and were able to stream freely through the universe, creating the cosmic microwave background as we know it. This left shells of baryonic matter at a fixed radius from the overdensities of dark matter, a distance known as the sound horizon. As time passed and the universe expanded, it was at these 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⁻¹ Mpc}}, (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.{{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 }}

Measuring the mass functions of galaxy clusters, which describe the number density of the clusters above a threshold mass, also provides evidence for dark energy {{explain|date=March 2018}}.{{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}} By comparing these mass functions at high and low redshifts to those predicted by different cosmological models, values for {{mvar|w}} and {{mvar|Ω_m}} are obtained which confirm a low matter density and a non-zero amount of dark energy.

{{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.

$$t\_0=\backslash int\_\{0\}^\{1\}\backslash frac\{da\}\{\backslash dot\{a\}\}$$

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

Recent discoveries of gravitational waves through LIGO and VIRGO{{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}}{{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}}{{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}} not only confirmed Einstein's predictions but also opened a new window into the universe. These gravitational waves can work as sort of standard sirens 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. 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 and will be dependent on other cosmological parameters like the dark energy density, matter density, etc. for distant sources.{{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}}

File:Dark Energy.jpg

{{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.

$$P=wc^2\backslash rho$$

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 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_λ > 0}}) and an accelerated expansion ({{math|q₀ < 0}}).

{{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.{{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 }} For example, for {{math|w {{=}} −{{sfrac|3|2}}}} and {{math|H₀}} =70 km·s⁻¹·Mpc⁻¹, the time remaining before the universe ends in this Big Rip is 22 billion years.{{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 }}

{{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, 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'.{{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 }}{{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 }} Dark fluid is an alternative explanation for accelerating expansion which attempts to unite dark matter and dark energy into a single framework.{{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 }} Alternatively, some authors have argued that the accelerated expansion of the universe could be due to a repulsive gravitational interaction of antimatter{{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}}{{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}}{{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 }} or a deviation of the gravitational laws from general relativity, such as massive gravity, meaning that gravitons themselves have mass.{{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}} 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.{{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 }}{{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}}{{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}} Another type of model, the backreaction conjecture,{{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 }}{{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 }} was proposed by cosmologist Syksy Räsänen:{{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}} 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.{{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 }} 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.

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.{{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 }} 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.{{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}}{{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 }} 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.

Although shockwave cosmology produces a universe that "looks essentially identical to the aftermath of the big bang",{{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}} 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.

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.{{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 }}{{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}}{{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}}{{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 }} 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.{{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}}{{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 }}{{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}} 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,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{{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 }} or that the supernova sample size used wasn't large enough.{{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}}{{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)}}

{{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) 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).

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.{{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 }}

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.John Baez, "The End of the Universe", 7 February 2016. http://math.ucr.edu/home/baez/end.html 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==

{{cols|colwidth=20em}}

• Cosmological constant
• Friedmann–Lemaître–Robertson–Walker metric
• High-Z Supernova Search Team
• Lambda-CDM model
• List of multiple discoveries
• Expansion of the universe
• Scale factor (cosmology)
• Supernova Cosmology Project
• Hubble constant

{{colend}}

{{Reflist|group=notes}}

{{Reflist|30em}}

{{Cosmology topics}}

{{Breakthrough of the Year}}

{{Portal bar|Physics|Astronomy|Stars|Outer space|Science}}

{{Authority control}}

Expansion of the universe

Category:Big Bang

Category:Physical cosmological concepts