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Theage of the universeis the time elapsed between theBig Bangand the present day. Current theory and observations suggest that theuniverseis between 13.5 and 14billionyears old.[1]The uncertainty range has been obtained by the agreement of a number of scientific research projects.Scientific instrumentsand methods have improved the ability to measure the age of the universe with a great accuracy. These projects includedbackground radiationmeasurementsand more ways to measure theexpansion of the universe. Background radiation measurements give the coolingtimeof the universe since thebig bang.Expansionof the universe measurements give accurate data to calculate the age of the universe.

Contents

[hide] 1Explanation 2Observational limits 3Cosmological parameters 4WMAP 5Assumption of strong priors 6See also 7References 8External links

[edit]ExplanationTheLambda-CDM concordance modeldescribes the evolution of the universe from a very uniform, hot, dense primordial state to its present state over a span of about 13.75 billion years ofcosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such asWMAP. In contrast, theories of the origin of the primordial state remain very speculative. If one extrapolates the Lambda-CDM model backward from the earliest well-understood state, it quickly (within a small fraction of a second) reaches asingularitycalled the "Big Bang singularity." This singularity is not considered to have any physical significance, 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, "106second after the Big Bang" is a well-defined era in the universe's evolution. In one sense it would be more meaningful to refer to the same era as "13.7 billion years minus 106seconds ago," but this is unworkable since the latter time interval is swamped by uncertainty in the former.

Though the universe might in theory have a longer history, cosmologists presently use "age of the universe" to mean the duration of the Lambda-CDM expansion, or equivalently the elapsed time since theBig Bang.

[edit]Observational limitsSince 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 coolestwhite dwarfs, and theturnoff pointof thered dwarfs. On April 23, 2009 agamma-ray burstwas detected which was later confirmed at being over 13 billion years old.[2][edit]Cosmological parameters

The age of the universe can be determined by measuring theHubble constanttoday and extrapolating back in time with the observed value of density parameters (). Before the discovery ofdark energy, it was believed that the universe was matter-dominated, and so on this graph corresponds tom. Note that theaccelerating universehas the greatest age, while theBig Crunchuniverse has the smallest age.

The value of the age correction factorFis shown as a function of two cosmological parameters: the current fractional matter densitymand cosmological constant density. Thebest-fit valuesof 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. Today this is largely carried out in the context of theCDMmodel, where the Universe is assumed to contain normal (baryonic) matter, colddark matter, radiation (including bothphotonsandneutrinos), and acosmological constant. The fractional contribution of each to the current energy density of the Universe is given by thedensity parametersm, r, and . The fullCDMmodel is described by a number of other parameters, but for the purpose of computing its age these three, along with theHubble parameterH0are the most important.

If one has accurate measurements of these parameters, then the age of the universe can be determined by using theFriedmann equation. This equation relates the rate of change in thescale factora(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 byintegratingthis formula. The aget0is then given by an expression of the form

where the functionFdepends 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 inverse of the Hubble parameter,

To get a more accurate number, the correction factorFmust 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 theWMAP values(m, ) = (0.266, 0.732), shown by the box in the upper left corner of the figure, this correction factor is nearly one:F= 0.996. 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, ris held constant (roughly equivalent to holding theCMBtemperature constant) and the curvature density parameter is fixed by the value of the other three.

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.CMBmeasurements are very good at constraining the matter content m[3]and curvature parameter k.[4]It is not as sensitive to directly,[4]partly because the cosmological constant only becomes important at low redshift. The most accurate determinations of the Hubble parameterH0come fromType 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, theBig Bang modelhad difficulty explaining whyglobular clustersin 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.[5]

HYPERLINK "http://en.wikipedia.org/wiki/Age_of_the_universe" \l "cite_note-5" [6]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.[7][edit]WMAPNASA'sWilkinson Microwave Anisotropy Probe(WMAP) project estimates the age of the universe to be:

(1.373 0.012) 1010years.

That is, the universe is about 13.73billionyearsold,[1]with an uncertainty of 120millionyears. 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.[8]This measurement is made by using the location of the first acoustic peak in themicrowave backgroundpower spectrum to determine the size of the decoupling surface (size of 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.[9]This is the value currently most quoted by astronomers.

[edit]Assumption of strong priorsCalculating the age of the universe is only accurate if the assumptions built into the models being used to estimate it are also accurate. This is referred to asstrong priorsand 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 WMAP data "only" is 13.690.13 Gyr[1](the slightly higher number of 13.73 includes some other data mixed in). This number represents the first accurate "direct" measurement of the age of the universe (other methods typically involveHubble's lawand 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. fromWMAP) therefore is to use aBayesian Statisticalanalysis, which normalizes the results based upon the priors (i.e. the model).[9]This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.[10]

HYPERLINK "http://en.wikipedia.org/wiki/Age_of_the_universe" \l "cite_note-10" [11][edit]See alsoAstronomy portal

Age of the Earth Metric expansion of space Red shift observations in astronomy Observable universe Anthropic principle Cosmology Hubble Deep Field[edit]References1. ^abc"Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results" (PDF). nasa.gov. Retrieved 2008-03-06.2. ^"http://news.bbc.co.uk/2/hi/science/nature/8022917.stm".2009-04-28. Retrieved 2009-04-28.3. ^"Animation: Matter Content Sensitivity. The matter-radiation ratio is raised while keeping all other parameters fixed (Omega_0h^2= 0.1-1) .". uchicago.edu. Retrieved 2008-02-23.4. ^ab"Animation:Angular diameter distance scaling with curvature and lambda (Omega_K=1-Omega_0-Omega_Lambda, fixed Omega_0h^2 and Omega_Bh^2)". uchicago.edu. Retrieved 2008-02-23.5. ^"Globular Star Clusters". seds.org. Retrieved 2008-02-23.6. ^"Independent age estimates". astro.ubc.ca. Retrieved 2008-02-23.7. ^J. P. Ostriker; Paul J. Steinhardt.COSMIC CONCORDANCE. Retrieved 2008-02-23.8. ^Francesco de Bernardis; A. Melchiorri, L. Verde, R. Jimenez.The Cosmic Neutrino Background and the age of the Universe. Retrieved 2008-02-23.9. ^abSpergel, D. N.; et al. (2003). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters".The Astrophysical Journal Supplement Series148: 175194.doi:10.1086/377226.10. ^Loredo, T. J. (PDF).The Promise of Bayesian Inference for Astrophysics. Retrieved 2008-02-23.11. ^Colistete, R.; J. C. Fabris & S. V. B. Concalves (2005). "Bayesian Statistics and Parameter Constraints on the Generalized Chaplygin Gas Model Using SNe ia Data".International Journal of Modern Physics D14(5): 775796.doi:10.1142/S0218271805006729.ariv:astro-ph/0409245. Retrieved 2008-02-23.[edit]External links Ned Wright's Cosmology Tutorial Wright, Edward L. (2 July2005). "Age of the Universe". Wayne Hu'scosmological parameter animations J. P. OstrikerandP. J. Steinhardt,Cosmic Concordance, arXiv:astro-ph/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.

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