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Age of the universe

From Wikipedia, the free encyclopedia
Cosmological time duration
This article is about scientific estimates of the age of the universe. For religious and other non-scientific estimates, seeDating creation.

Part of a series on
Physical cosmology
Full-sky image derived from nine years' WMAP data

InBig Bang models ofphysical cosmology, theage of the universe is thecosmological time back to the point when thescale factor of theuniverse extrapolates to zero.[1] Modern models calculate the age now as 13.79 billion years.[2] Astronomers have two different approaches to determine the age of theuniverse. One is based on a particle physics model of the early universe calledLambda-CDM, matched to measurements of the distant, and thus old features, like thecosmic microwave background. The other is based on the distance and relative velocity of a series or "ladder" of different kinds of stars, making it depend on local measurements late in the history of the universe.[3] These two methods give slightly different values for theHubble constant, which is then used in a formula to calculate the age. The range of the estimate is also within the range of the estimate for theoldest observed star in the universe.[4]

History

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Main articles:Cosmic age problem andCosmic microwave background
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In the 18th century, the concept that theage of Earth was millions, if not billions, of years began to appear. Nonetheless, most scientists throughout the 19th century and into the first decades of the 20th century presumed that the universe itself wassteady state and eternal, possibly with stars coming and going but no changes occurring at the largest scale known at the time.[5]

The first scientific theories indicating that the age of the universe might be finite were the studies ofthermodynamics, formalized in the mid-19th century. The concept ofentropy dictates that if the universe (or any other closed system) were infinitely old, then everything inside would be at the same temperature, and thus there would be no stars and no life. No scientific explanation for this contradiction was put forth at the time.

In 1915,Albert Einstein published the theory ofgeneral relativity[6] and in 1917 constructed the firstcosmological model based on his theory. In order to remain consistent with a steady-state universe, Einstein added what was later called acosmological constant to his equations. Einstein's model of a static universe was proved unstable byArthur Eddington.

The first direct observational hint that the universe was not static but expanding came from the observations of 'recession velocities', mostly byVesto M. Slipher, combined with distances to the 'nebulae' (galaxies) byEdwin Hubble in a work published in 1929.[7] Earlier in the 20th century, Hubble and others resolved individual stars within certain nebulae, thus determining that they were galaxies, similar to, but external to, theMilky Way Galaxy. In addition, these galaxies were very large and very far away.Spectra taken of these distant galaxies showed ared shift in theirspectral lines presumably caused by theDoppler effect, thus indicating that these galaxies were moving away from the Earth. In addition, the farther away these galaxies seemed to be (the dimmer they appeared) the greater was their redshift, and thus the faster they seemed to be moving away. This was the first direct evidence that the universe is not static but expanding. The first estimate of the age of the universe came from the calculation of when all of the objects must have started speeding out from the same point. Hubble's initial value for the universe's age was very low, as the galaxies were assumed to be much closer than later observations found them to be.

Thelookback time of extragalactic observations by their redshift up toz = 20[8]

The first reasonably accurate measurement of the rate of expansion of the universe, theHubble constant, was made in 1958 by astronomerAllan Sandage.[9] His measured value for the Hubble constant came very close to the value range generally accepted since then.

Sandage, like Einstein, did not believe his own results at the time of discovery.[citation needed] Sandage proposed new theories ofcosmogony to explain this discrepancy. This issue was more or less resolved by improvements in the theoretical models used for estimating the ages of stars. As of 2024, using the latest models for stellar evolution, the estimated age of theoldest known star is13.8±4 billion years.[10]

The discovery ofcosmic microwave background radiation announced in 1965[11] finally brought an effective end to the remaining scientific uncertainty over the expanding universe. It was a chance result from work by two teams less than 60 miles apart. In 1964,Arno Penzias andRobert Woodrow Wilson were trying to detectradio waveechoes with a supersensitive antenna. The antenna persistently detected a low, steady, mysteriousnoise in themicrowave region that was evenly spread over the sky, and was present day and night. After testing, they became certain that the signal did not come from theEarth, theSun, or theMilky Way galaxy, but from outside the Milky Way, but could not explain it. At the same time another team,Robert H. Dicke,Jim Peebles, andDavid Wilkinson, were attempting to detect low level noise that might be left over from theBig Bang and could prove whether the Big Bang theory was correct. The two teams realized that the detected noise was in fact radiation left over from the Big Bang, and that this was strong evidence that the theory was correct. Since then, a great deal of other evidence has strengthened and confirmed this conclusion, and refined the estimated age of the universe.

The space probes WMAP, launched in 2001, andPlanck, launched in 2009, produced data that determines the Hubble constant and the age of the universe independent of galaxy distances, removing the largest source of error.[12]

Definition

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Relationship between redshift and age of the universe, fromz = 5...20[8]

Experimental observations confirm expansion of universe according toHubble's law. Since the universe is expanding, the equation for that expansion can be "run backwards" to its starting point. TheLambda-CDM concordance model describes the expansion of the universe from a very uniform, hot, dense primordial state to its existing state over a span of about 13.77 billion years[13] ofcosmological time. This model is well understood theoretically and strongly supported by recent high-precisionastronomical observations such asWMAP. TheInternational Astronomical Union uses the term "age of the universe" to mean the duration of the Lambda-CDM expansion,[14] or equivalently, the time elapsed within theobservable universe since the Big Bang. The expansion rate at any timet{\displaystyle t} is called theHubble parameterH(t)≡a˙a,{\displaystyle H(t)\equiv {\frac {\dot {a}}{a}},}which is modeled asH(a)≡a˙a=H0Ωma−3+Ωrada−4+ΩΛ+(1−Ωm−Ωrad−ΩΛ)a−2,{\displaystyle H(a)\equiv {\frac {\dot {a}}{a}}=H_{0}{\sqrt {\Omega _{\rm {m}}a^{-3}+\Omega _{\mathrm {rad} }a^{-4}+\Omega _{\Lambda }+(1-\Omega _{\rm {m}}-\Omega _{\mathrm {rad} }-\Omega _{\Lambda })a^{-2}}},}whereΩx{\displaystyle \Omega _{x}} are density parameters, withm{\displaystyle \mathrm {m} } for mass (baryons andcold dark matter),rad{\displaystyle \mathrm {rad} } forradiation (photons plus relativisticneutrinos), andΛ{\displaystyle \Lambda } fordark energy. The valueH0{\displaystyle H_{0}}, called theHubble constant, is the Hubble parameter (t=0{\displaystyle t=0}) and it has units of inverse time. The age of the universe is then defined as[15]: 512 tage=1H0∫01daΩma−1+Ωrada−2+ΩΛa2+(1−Ωm−Ωrad−ΩΛ),{\displaystyle t_{\textrm {age}}={\frac {1}{H_{0}}}\int _{0}^{1}{\frac {da}{\sqrt {\Omega _{\rm {m}}a^{-1}+\Omega _{\mathrm {rad} }a^{-2}+\Omega _{\Lambda }a^{2}+(1-\Omega _{\rm {m}}-\Omega _{\mathrm {rad} }-\Omega _{\Lambda })}}},}The integral is close to 1 soH0−1{\displaystyle H_{0}^{-1}} is close to the age of the universe.

Observational limits

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Since the universe must be at least as old as the oldest things in it, there are a number of observations that put a lower limit on the age of the universe;[16][17] these include

  • the temperature of the coolestwhite dwarfs, which gradually cool as they age, and
  • the dimmestturnoff point ofmain sequencestars in clusters (lower-mass stars spend a greater amount of time on the main sequence, so the lowest-mass stars that have evolved away from the main sequence set a minimum age).

Before the incorporation ofdark energy in the model of cosmic expansion, the age was awkwardly less than the oldest observed astronomical objects. This connection can be used in reverse: the oldest objects found constrain the values of the density parameter for dark energy.[15]: 513 

Cosmological parameters

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The age of the universe can be determined by measuring theHubble constant and extrapolating back in time with the observed value of density parameters ( Ω {\displaystyle ~\Omega ~}). Before the discovery ofdark energy, it was believed that the universe was matter-dominated (Einstein–de Sitter universe, green curve). Thede Sitter universe has infinite age, while theclosed universe has the least age.
The value of the age correction factor, F ,{\displaystyle ~F~,} is shown as a function of twocosmological parameters: the fractional matter density Ωm {\displaystyle ~\Omega _{\text{m}}~} and cosmological constant density ΩΛ .{\displaystyle ~\Omega _{\Lambda }~.} Thebest-fit values of these parameters are shown by the box in the upper left; the matter-dominated universe is shown by the star in the lower right.

The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. This is largely carried out in the context of theΛCDM model, where the universe is assumed to contain normal (baryonic) matter, colddark matter, radiation (including bothphotons andneutrinos), and acosmological constant.[18]

The fractional contribution of each to the energy density of the universe is given by thedensity parameters Ωm ,{\displaystyle ~\Omega _{\text{m}}~,} Ωr ,{\displaystyle ~\Omega _{\text{r}}~,} and ΩΛ .{\displaystyle ~\Omega _{\Lambda }~.} The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with theHubble parameter H0 {\displaystyle ~H_{0}~}, are the most important.

With accurate measurements of these parameters, the age of the universe can be determined by using theFriedmann equation. This equation relates the rate of change in thescale factor a(t) {\displaystyle ~a(t)~}to the matter content of the universe. Turning this relation around, we can calculate the change in time per change in scale factor and thus calculate the total age of the universe byintegrating this formula. The age t0 {\displaystyle ~t_{0}~}is then given by an expression of the form

t0=1H0F(Ωr,Ωm,ΩΛ,…) {\displaystyle t_{0}={\frac {1}{H_{0}}}\,F(\,\Omega _{\text{r}},\,\Omega _{\text{m}},\,\Omega _{\Lambda },\,\dots \,)~}

where H0 {\displaystyle ~H_{0}~}is the Hubble parameter and the function F {\displaystyle ~F~}depends only on the fractional contribution to the universe's energy content that comes from various components. The first observation that one can make from this formula is that it is the Hubble parameter that controls that age of the universe, with a correction arising from the matter and energy content. So a rough estimate of the age of the universe comes from theHubble time, the inverse of the Hubble parameter. With a value for H0 {\displaystyle ~H_{0}~}around69 km/s/Mpc, the Hubble time evaluates to 1/H0= {\displaystyle ~1/H_{0}=~}14.5 billion years.[19]

To get a more accurate number, the correction function F {\displaystyle ~F~}must be computed. In general this must be done numerically, and the results for a range of cosmological parameter values are shown in the figure. For thePlanck values (Ωm,ΩΛ)= {\displaystyle ~(\Omega _{\text{m}},\Omega _{\Lambda })=~}(0.3086, 0.6914), shown by the box in the upper left corner of the figure, this correction factor is about F=0.956 .{\displaystyle ~F=0.956~.} For a flat universe without any cosmological constant, shown by the star in the lower right corner, F=2/3 {\displaystyle ~F={2}/{3}~}is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure, Ωr {\displaystyle ~\Omega _{\text{r}}~}is held constant (roughly equivalent to holding thecosmic microwave background temperature constant) and the curvature density parameter is fixed by the value of the other three.

Apart from the Planck satellite, the Wilkinson Microwave Anisotropy Probe (WMAP) was instrumental in establishing an accurate age of the universe, though other measurements must be folded in to gain an accurate number.CMB measurements are very good at constraining the matter content Ωm ,{\displaystyle ~\Omega _{\text{m}}~,}[20] and curvature parameter Ωk .{\displaystyle ~\Omega _{\text{k}}~.}[21] It is not as sensitive to ΩΛ {\displaystyle ~\Omega _{\Lambda }~}directly,[21] partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter H0 {\displaystyle ~H_{0}~}are believed to come from measured brightnesses and redshifts of distantType Ia supernovae. Combining these measurements leads to the generally accepted value for the age of the universe quoted above.

The cosmological constant makes the universe "older" for fixed values of the other parameters. This is significant, since before the cosmological constant became generally accepted, the Big Bang model had difficulty explaining whyglobular clusters in the Milky Way appeared to be far older than the age of the universe as calculated from the Hubble parameter and a matter-only universe.[22][23] Introducing the cosmological constant allows the universe to be older than these clusters, as well as explaining other features that the matter-only cosmological model could not.[24]

Lookback time

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Light observed from astronomical objects was emitted when the universe was younger. Astronomers uselookback time,tL{\displaystyle t_{L}}, to describe the difference in the age of the universe here and now,[25]t0{\displaystyle t_{0}}, from the age at the time of emission,te{\displaystyle t_{e}}:tL(z)=t0−te(z){\displaystyle t_{L}(z)=t_{0}-t_{e}(z)}wheret is an age.The lookback time depends on the object's redshift and, like the age of the universe, the cosmological parameters selected.[25]

WMAP

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NASA'sWilkinson Microwave Anisotropy Probe (WMAP) project'snine-year data release in 2012 estimated the age of the universe to be(13.772±0.059)×109 years (13.772 billion years, with an uncertainty of plus or minus 59 million years).[26]

This age is based on the assumption that the project's underlying model is correct; other methods of estimating the age of the universe could give different ages. Assuming an extra background of relativistic particles, for example, can enlarge the error bars of the WMAP constraint by one order of magnitude.[27]

This measurement is made by using the location of the first acoustic peak in themicrowave background power spectrum to determine the size of the decoupling surface (size of the universe at the time of recombination). The light travel time to this surface (depending on the geometry used) yields a reliable age for the universe. Assuming the validity of the models used to determine this age, the residual accuracy yields a margin of error near one per cent.[12]

Planck

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In 2015, thePlanck Collaboration estimated the age of the universe to be13.813±0.038 billion years, slightly higher but within the uncertainties of the earlier number derived from the WMAP data.[28]

In the table below, figures are within 68%confidence limits for the base ΛCDM model.

Cosmological parameters from 2015 Planck results[28]
ParameterSymbolTT + lowPTT + lowP + lensingTT + lowP + lensing + extTT, TE, EE + lowPTT, TE, EE + lowP + lensingTT, TE, EE + lowP + lensing + ext
Age of the universe
(Ga)		t0{\displaystyle t_{0}}13.813±0.03813.799±0.03813.796±0.02913.813±0.02613.807±0.02613.799±0.021
Hubble constant
(km⁄Mpc⋅s)		H0{\displaystyle H_{0}}67.31±0.9667.81±0.9267.90±0.5567.27±0.6667.51±0.6467.74±0.46

Legend:

In 2018, the Planck Collaboration updated its estimate for the age of the universe to13.787±0.020 billion years.[2]

Assumption of strong priors

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Calculating the age of the universe is accurate only if the assumptions built into the models being used to estimate it are also accurate. This is referred to asstrong priors and essentially involves stripping the potential errors in other parts of the model to render the accuracy of actual observational data directly into the concluded result. The age given is thus accurate to the specified error, since this represents the error in the instrument used to gather the raw data input into the model.

The age of the universe based on the best fit toPlanck 2018 data alone is13.787±0.020 billion years. A component to the analysis of data used to determine the age of the universe (e.g. fromPlanck) is to use aBayesian statistical analysis, which normalizes the results based upon the priors (i.e. the model).[12] This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.[29][30]

See also

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References

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  1. ^Kolb, Edward; Turner, Michael S. (2018).The Early Universe. Boulder: Chapman and Hall/CRC.ISBN 978-0-201-62674-2.
  2. ^abPlanck Collaboration (2020)."Planck 2018 results. VI. Cosmological parameters".Astronomy & Astrophysics.641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column).arXiv:1807.06209.Bibcode:2020A&A...641A...6P.doi:10.1051/0004-6361/201833910.S2CID 119335614.
  3. ^Verde, Licia; Schöneberg, Nils; Gil-Marín, Héctor (13 September 2024)."A Tale of Many H0".Annual Review of Astronomy and Astrophysics.62:287–331.doi:10.1146/annurev-astro-052622-033813.ISSN 0066-4146.
  4. ^Vagnozzi, Sunny; Pacucci, Fabio; Loeb, Abraham (1 November 2022)."Implications for the Hubble tension from the ages of the oldest astrophysical objects".Journal of High Energy Astrophysics.36:27–35.arXiv:2105.10421.Bibcode:2022JHEAp..36...27V.doi:10.1016/j.jheap.2022.07.004.ISSN 2214-4048.
  5. ^Heilborn, J. L., ed. (2005).The Oxford Guide to the History of Physics and Astronomy. Oxford University Press. p. 312.ISBN 978-0-19-517198-3.
  6. ^Einstein, Albert (1915). "Zur allgemeinen Relativitätstheorie" [On the general theory of relativity].Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (in German):778–786.Bibcode:1915SPAW.......778E.
  7. ^Hubble, E. (1929)."A relation between distance and radial velocity among extra-galactic nebulae".Proceedings of the National Academy of Sciences.15 (3):168–173.Bibcode:1929PNAS...15..168H.doi:10.1073/pnas.15.3.168.PMC 522427.PMID 16577160.
  8. ^abPilipenko, Sergey V. (2013). "Paper-and-pencil cosmological calculator".arXiv:1303.5961 [astro-ph.CO]..Fortran-90 code upon which the citing charts and formulae are based.
  9. ^Sandage, A. R. (1958). "Current Problems in the Extragalactic Distance Scale".The Astrophysical Journal.127 (3):513–526.Bibcode:1958ApJ...127..513S.doi:10.1086/146483.
  10. ^Cowan, John J.; Sneden, Christopher; Burles, Scott; Ivans, Inese I.; Beers, Timothy C.; Truran, James W.; et al. (June 2002). "The Chemical Composition and Age of the Metal-poor Halo Star BD +17°3248".The Astrophysical Journal.572 (2):861–879.arXiv:astro-ph/0202429.Bibcode:2002ApJ...572..861C.doi:10.1086/340347.S2CID 119503888.
  11. ^Penzias, A. A.; Wilson, R .W. (1965)."A Measurement of Excess Antenna Temperature at 4080 Mc/s".The Astrophysical Journal.142:419–421.Bibcode:1965ApJ...142..419P.doi:10.1086/148307.
  12. ^abcSpergel, D.N.; et al. (2003). "First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters".The Astrophysical Journal Supplement Series.148 (1):175–194.arXiv:astro-ph/0302209.Bibcode:2003ApJS..148..175S.doi:10.1086/377226.S2CID 10794058.
  13. ^"Cosmic Detectives".European Space Agency. 2 April 2013. Retrieved15 April 2013.
  14. ^Chang, K. (9 March 2008)."Gauging age of universe becomes more precise".The New York Times.
  15. ^abZee, A. (2013).Einstein gravity in a nutshell. Princeton: Princeton University Press.ISBN 978-0-691-14558-7.
  16. ^Chaboyer, Brian (1 December 1998). "The age of the universe".Physics Reports.307 (1–4):23–30.arXiv:astro-ph/9808200.Bibcode:1998PhR...307...23C.doi:10.1016/S0370-1573(98)00054-4.S2CID 119491951.
  17. ^Chaboyer, Brian (16 February 1996). "A Lower Limit on the Age of the Universe".Science.271 (5251):957–961.arXiv:astro-ph/9509115.Bibcode:1996Sci...271..957C.doi:10.1126/science.271.5251.957.S2CID 952053.
  18. ^See Chapter 25 Cosmological Parameters in S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
  19. ^Liddle, A. R. (2003).An Introduction to Modern Cosmology (2nd ed.).Wiley. p. 57.ISBN 978-0-470-84835-7.
  20. ^Hu, W."Animation: Matter Content Sensitivity. The matter-radiation ratio is raised while keeping all other parameters fixed".University of Chicago.Archived from the original on 23 February 2008. Retrieved23 February 2008.
  21. ^abHu, W."Animation: Angular diameter distance scaling with curvature and lambda".University of Chicago.Archived from the original on 23 February 2008. Retrieved23 February 2008.
  22. ^"Globular Star Clusters".SEDS. 1 July 2011. Archived fromthe original on 24 February 2008. Retrieved19 July 2013.
  23. ^Iskander, E. (11 January 2006)."Independent age estimates".University of British Columbia.Archived from the original on 6 March 2008. Retrieved23 February 2008.
  24. ^Ostriker, J. P.; Steinhardt, P. J. (1995). "Cosmic concordance".arXiv:astro-ph/9505066.
  25. ^abSee the standard reference work:Hogg, D.W. (1999). "Distance measures in cosmology".arXiv:astro-ph/9905116.
  26. ^Bennett, C. L.; et al. (2013). "Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps and results".The Astrophysical Journal Supplement Series.208 (2): 20.arXiv:1212.5225.Bibcode:2013ApJS..208...20B.doi:10.1088/0067-0049/208/2/20.S2CID 119271232.
  27. ^de Bernardis, F.; Melchiorri, A.; Verde, L.; Jimenez, R. (2008). "The Cosmic Neutrino Background and the Age of the Universe".Journal of Cosmology and Astroparticle Physics.2008 (3): 20.arXiv:0707.4170.Bibcode:2008JCAP...03..020D.doi:10.1088/1475-7516/2008/03/020.S2CID 8896110.
  28. ^abPlanck Collaboration (2016)."Planck 2015 results. XIII. Cosmological parameters".Astronomy & Astrophysics.594. page A13 (see PDF page 32, Table 4: "Age/Gyr", last column).arXiv:1502.01589.Bibcode:2016A&A...594A..13P.doi:10.1051/0004-6361/201525830.S2CID 119262962.
  29. ^Loredo, T. J. (1992)."The Promise of Bayesian Inference for Astrophysics"(PDF). In Feigelson, E. D.; Babu, G. J. (eds.).Statistical Challenges in Modern Astronomy.Springer-Verlag. pp. 275–297.Bibcode:1992scma.conf..275L.doi:10.1007/978-1-4613-9290-3_31.ISBN 978-1-4613-9292-7.
  30. ^Colistete, R.; Fabris, J. C.; Concalves, S. V. B. (2005). "Bayesian statistics and parameter constraints on the generalized Chaplygin gas model Using SNe ia data".International Journal of Modern Physics D.14 (5):775–796.arXiv:astro-ph/0409245.Bibcode:2005IJMPD..14..775C.doi:10.1142/S0218271805006729.S2CID 14184379.

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