Age of the universe
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In physical cosmology, the age of the universe is the time elapsed since the Big Bang. The current measurement of the age of the universe is ±0.021 billion years ( 13.799±0.021)×10^{9} years) within the (13.799LambdaCDM concordance model.^{[1]}^{[2]} The uncertainty of 21 million years has been obtained by the agreement of a number of scientific research projects, such as microwave background radiation measurements by the Planck satellite, the Wilkinson Microwave Anisotropy Probe and other probes. Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang,^{[3]} and measurements of the expansion rate of the universe can be used to calculate its approximate age by extrapolating backwards in time.
Explanation
The LambdaCDM concordance model describes the evolution of the universe from a very uniform, hot, dense primordial state to its present state over a span of about 13.8 billion years^{[4]} of cosmological time. This model is well understood theoretically and strongly supported by recent highprecision astronomical observations such as WMAP. In contrast, theories of the origin of the primordial state remain very speculative. If one extrapolates the LambdaCDM model backward from the earliest wellunderstood state, it quickly (within a small fraction of a second) reaches a singularity called the "Big Bang singularity". This singularity is not understood as having a physical significance in the usual sense, but it is convenient to quote times measured "since the Big Bang" even though they do not correspond to a physically measurable time. For example, "10^{−6} seconds after the Big Bang" is a welldefined era in the universe's evolution. If one referred to the same era as "13.8 billion years minus 10^{−6} seconds ago", the precision of the meaning would be lost because the minuscule latter time interval is swamped by uncertainty in the former.
Though the universe might in theory have a longer history, the International Astronomical Union^{[5]} presently use "age of the universe" to mean the duration of the LambdaCDM expansion, or equivalently the elapsed time since the Big Bang in the current observable universe.
Observational limits
Since the universe must be at least as old as the oldest thing in it, there are a number of observations which put a lower limit on the age of the universe; these include the temperature of the coolest white dwarfs, which gradually cool as they age, and the dimmest turnoff point of main sequence stars in clusters (lowermass stars spend a greater amount of time on the main sequence, so the lowestmass stars that have evolved off of the main sequence set a minimum age).
Cosmological parameters
The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. Today this is largely carried out in the context of the ΛCDM model, where the universe is assumed to contain normal (baryonic) matter, cold dark matter, radiation (including both photons and neutrinos), and a cosmological constant. The fractional contribution of each to the current energy density of the universe is given by the density parameters Ω_{m}, Ω_{r}, and Ω_{Λ}. The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter , are the most important.
If one has accurate measurements of these parameters, then the age of the universe can be determined by using the Friedmann equation. This equation relates the rate of change in the scale factor 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 by integrating this formula. The age t_{0} is then given by an expression of the form
where is the Hubble parameter and the function 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 the Hubble time, the inverse of the Hubble parameter. With a value for around km/s/Mpc, the Hubble time evaluates to = 68 billion years.^{[6]} 14.4
To get a more accurate number, the correction factor 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 the Planck values (Ω_{m}, Ω_{Λ}) = (0.3086, 0.6914), shown by the box in the upper left corner of the figure, this correction factor is about F = 0.956. For a flat universe without any cosmological constant, shown by the star in the lower right corner, F = ^{2}⁄_{3} is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure, Ω_{r} is held constant (roughly equivalent to holding the CMB 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 Ω_{m}^{[7]} and curvature parameter Ω_{k}.^{[8]} It is not as sensitive to Ω_{Λ} directly,^{[8]} partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter H_{0} come from Type 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 why globular clusters in the Milky Way appeared to be far older than the age of the universe as calculated from the Hubble parameter and a matteronly universe.^{[9]}^{[10]} Introducing the cosmological constant allows the universe to be older than these clusters, as well as explaining other features that the matteronly cosmological model could not.^{[11]}
WMAP
NASA's Wilkinson Microwave Anisotropy Probe (WMAP) project's nineyear data release in 2012 estimated the age of the universe to be ±0.059)×10^{9} years (13.772 billion years, with an uncertainty of plus or minus 59 million years).^{[3]} (13.772
However, 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.^{[12]}
This measurement is made by using the location of the first acoustic peak in the microwave 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 percent.^{[13]}
Planck
In 2015, the Planck Collaboration estimated the age of the universe to be ±0.038 billion years, slightly higher but within the uncertainties of the earlier number derived from the WMAP data. By combining the Planck data with external data, the best combined estimate of the age of the universe is 13.813±0.021)×10^{9} years old.^{[1]}^{[2]} (13.799
Parameter  Symbol  TT+lowP 68% limits  TT+lowP +lensing 68% limits  TT+lowP +lensing+ext 68% limits  TT,TE,EE+lowP 68% limits  TT,TE,EE+lowP +lensing 68% limits  TT,TE,EE+lowP +lensing+ext 68% limits 

Age of the universe (Ga)  ±0.038 13.813  ±0.038 13.799  ±0.029 13.796  ±0.026 13.813  ±0.026 13.807  ±0.021 13.799  
Hubble constant ( ^{km}⁄_{Mpc•s} )  ±0.96 67.31  ±0.92 67.81  ±0.55 67.90  ±0.66 67.27  ±0.64 67.51  ±0.46 67.74 
Assumption of strong priors
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 as strong 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. Although this is not a valid procedure in all contexts (as noted in the accompanying caveat: "based on the fact we have assumed the underlying model we used is correct"), the age given is thus accurate to the specified error (since this error 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 to Planck 2015 data alone is ±0.038 billion years (the estimate of 13.813±0.021 billion years uses Gaussian 13.799priors based on earlier estimates from other studies to determine the combined uncertainty). This number represents an accurate "direct" measurement of the age of the universe (other methods typically involve Hubble's law and the age of the oldest stars in globular clusters, etc.). It is possible to use different methods for determining the same parameter (in this case – the age of the universe) and arrive at different answers with no overlap in the "errors". To best avoid the problem, it is common to show two sets of uncertainties; one related to the actual measurement and the other related to the systematic errors of the model being used.
An important component to the analysis of data used to determine the age of the universe (e.g. from Planck) therefore is to use a Bayesian statistical analysis, which normalizes the results based upon the priors (i.e. the model).^{[13]} This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.^{[14]}^{[15]}
History
In the 18th century, the concept that the age of the Earth was millions, if not billions, of years began to appear. However, most scientists throughout the 19th century and into the first decades of the 20th century presumed that the universe itself was Steady State and eternal, with maybe stars coming and going but no changes occurring at the largest scale known at the time.
The first scientific theories indicating that the age of the universe might be finite were the studies of thermodynamics, formalized in the mid19th century. The concept of entropy 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 of general relativity^{[16]} and in 1917 constructed the first cosmological model based on his theory. In order to remain consistent with a steady state universe, Einstein added what was later called a cosmological constant to his equations. However, already in 1922, also using Einstein's theory, Alexander Friedmann, and independently five years later Georges Lemaître, showed that the universe cannot be static and must be either expanding or contracting. Einstein's model of a static universe was in addition proved unstable by Arthur Eddington.
The first direct observational hint that the universe has a finite age came from the observations of 'recession velocities', mostly by Vesto Slipher, combined with distances to the 'nebulae' (galaxies) by Edwin Hubble in a work published in 1929.^{[17]} 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, our Milky Way Galaxy. In addition, these galaxies were very large and very far away. Spectra taken of these distant galaxies showed a red shift in their spectral lines presumably caused by the Doppler 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 to us) 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.
The first reasonably accurate measurement of the rate of expansion of the universe, a numerical value now known as the Hubble constant, was made in 1958 by astronomer Allan Sandage.^{[18]} His measured value for the Hubble constant came very close to the value range generally accepted today.
However Sandage, like Einstein, did not believe his own results at the time of discovery. His value for the age of the universe was too short to reconcile with the 25billionyear age estimated at that time for the oldest known stars. Sandage and other astronomers repeated these measurements numerous times, attempting to reduce the Hubble constant and thus increase the resulting age for the universe. Sandage even proposed new theories of cosmogony to explain this discrepancy. This issue was finally resolved by improvements in the theoretical models used for estimating the ages of stars. As of 2013, using the latest models for stellar evolution, the estimated age of the oldest known star is ±0.8 billion years.^{[19]} 14.46
The discovery of microwave cosmic background radiation announced in 1965^{[20]} finally brought an effective end to the remaining scientific uncertainty over the expanding universe. The recently launched space probes WMAP, launched in 2001, and Planck, 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.^{[13]}
See also
 Age of the Earth
 Timeline of the far future: expected remaining lifetime of the Earth; our solar system; the universe
 Anthropic principle
 Cosmic Calendar (age of universe scaled to a single year)
 Cosmology
 Dark Ages Radio Explorer (DARE)
 Hubble Deep Field
 Illustris project
 Metric expansion of space
 Multiverse
 Observable universe
 Red shift observations in astronomy
 Static universe
 The First Three Minutes (1977 book by Steven Weinberg).
References
 1 2 3 Planck Collaboration (2015). "Planck 2015 results. XIII. Cosmological parameters (See PDF, page 32, Table 4, Age/Gyr, last column).". arXiv:1502.01589.
 1 2 Lawrence, C. R. (18 March 2015). "Planck 2015 Results" (PDF). Retrieved 24 November 2016.
 1 2 Bennett, C.L.; et al. (2013). "NineYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results". arXiv:1212.5225 [astroph.CO].
 ↑ "Cosmic Detectives". European Space Agency. 2 April 2013. Retrieved 20130415.
 ↑ Chang, K. (9 March 2008). "Gauging Age of Universe Becomes More Precise". The New York Times.
 ↑ Liddle, A. R. (2003). An Introduction to Modern Cosmology (2nd ed.). Wiley. p. 57. ISBN 0470848359.
 ↑ Hu, W. "Animation: Matter Content Sensitivity. The matterradiation ratio is raised while keeping all other parameters fixed.". University of Chicago. Archived from the original on 23 February 2008. Retrieved 20080223.
 1 2 Hu, W. "Animation: Angular diameter distance scaling with curvature and lambda". University of Chicago. Archived from the original on 23 February 2008. Retrieved 20080223.
 ↑ "Globular Star Clusters". SEDS. 1 July 2011. Archived from the original on 24 February 2008. Retrieved 20130719.
 ↑ Iskander, E. (11 January 2006). "Independent age estimates". University of British Columbia. Archived from the original on 6 March 2008. Retrieved 20080223.
 ↑ Ostriker, J. P.; Steinhardt, P. J. (1995). "Cosmic Concordance". arXiv:astroph/9505066.
 ↑ 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:10.1088/14757516/2008/03/020.
 1 2 3 Spergel, D. N.; et al. (2003). "FirstYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters". The Astrophysical Journal Supplement Series. 148 (1): 175–194. arXiv:astroph/0302209. Bibcode:2003ApJS..148..175S. doi:10.1086/377226.
 ↑ Loredo, T. J. (1992). "The Promise of Bayesian Inference for Astrophysics" (PDF). In Feigelson, E. D.; Babu, G. J. Statistical Challenges in Modern Astronomy. SpringerVerlag. pp. 275–297. Bibcode:1992scma.conf..275L. doi:10.1007/9781461392903_31. ISBN 9781461392927.
 ↑ 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:astroph/0409245. Bibcode:2005IJMPD..14..775C. doi:10.1142/S0218271805006729.
 ↑ Einstein, A. (1915). "Zur allgemeinen Relativitätstheorie". Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (in German): 778–786. Bibcode:1915SPAW.......778E.
 ↑ Hubble, E. (1929). "A relation between distance and radial velocity among extragalactic 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.
 ↑ 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.
 ↑ Bond, H. E.; Nelan, E. P.; Vandenberg, D. A.; Schaefer, G. H.; Harmer, D. (2013). "HD 140283: A Star in the Solar Neighborhood that Formed Shortly After the Big Bang". The Astrophysical Journal. 765 (12): L12. arXiv:1302.3180. Bibcode:2013ApJ...765L..12B. doi:10.1088/20418205/765/1/L12.
 ↑ 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.
External links
 Ned Wright's Cosmology Tutorial
 Wright, Edward L. (2 July 2005). "Age of the Universe".
 Wayne Hu's cosmological parameter animations
 Ostriker; Steinhardt (1995). "Cosmic Concordance". arXiv:astroph/9505066.
 SEDS page on "Globular Star Clusters"
 Douglas Scott "Independent Age Estimates"
 KryssTal "The Scale of the Universe" Space and Time scaled for the beginner.
 iCosmos: Cosmology Calculator (With Graph Generation )
 The Expanding Universe (American Institute of Physics)