age of the universe
| Physical cosmology |
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| Key topics |
| Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe |
| Early universe |
| Inflation · Nucleosynthesis GWB · Neutrino Background Cosmic microwave background |
| Expanding universe |
| Redshift · Hubble's law Metric expansion of space Friedmann equations FLRW metric |
| Structure formation |
| Shape of the universe Structure formation Galaxy formation Large-scale structure |
| Components |
| Lambda-CDM model Dark energy · Dark matter |
| History |
| Timeline of cosmology... |
| Cosmology experiments |
| Observational cosmology 2dF · SDSS CoBE · BOOMERanG · WMAP |
| Scientists |
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Einstein · Hawking . Friedman · Lemaître · Hubble · Penzias · Wilson · Gamow · Dicke · Zel'dovich · Mather · Smoot · others |
The age of the universe, in physics, is the time elapsed between the Big Bang and the present day. Current observations suggest that this is about 13.7 billion years, with an uncertainty of about +/-200 million years.
Observational limits on the age of the universe
Since the universe must be older than the oldest thing in it, there are a number of observations which limit the age of the universe. These include the temperature of the coolest white dwarfs, and the turnoff point of the red dwarfs.
Explanation
The Lambda-CDM 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 13.7 billion years of cosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such as WMAP. In contrast, theories of the origin of the primordial state remain very speculative. The dominant theory, inflation, as well as the recent ekpyrotic scenario, suggest that the Big Bang cosmos that we observe may be a part of a larger universe with very different physical properties and with a history extending back longer than 13.7 billion years. It is not yet clear whether these ideas are testable, even in principle.
If one extrapolates the Lambda-CDM model backward from the earliest well-understood state, it quickly (within a small fraction of a second) reaches a mathematical singularity called 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, "10−6 second 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 10−6 seconds 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 the Big Bang.
Age as a function of 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 Ωm, Ωr, and ΩΛ. 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 H0 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 t0 is then given by an expression of the form,
where 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 inverse of the Hubble parameter,
- Failed to parse (unknown function\text): \frac{1}{H_0} = \left( \frac{H_0}{72\quad\text{km/(s}\cdot\text{Mpc)} } \right)^{-1} \times 13.6 \quad\text{Gyr}
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 is shown in the figure. For the
WMAP values (Ωm,ΩΛ) = (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, Ωr 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.
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 [1] and curvature parameter Ωk [2]. It is not as sensitive to ΩΛ directly [3], partly because the cosmological constant only becomes important at low redshift. The most accurate determinations of the Hubble parameter H0 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 matter-only universe [4] [5]. 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 [6].
Age based on WMAP
NASA's Wilkinson Microwave Anisotropy Probe (WMAP) project estimates the age of the universe to be:
- (13.7 ± 0.2) × 109 years.
That is, the universe is about 13.7 billion years old,[1] with an uncertainty of 200 million years. 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, (see F De bernardis, A. Melchiorri, L. Verde, R. Jimenez, http://xxx.arxiv.org/abs/0707.4170) can enlarge the error bars of the WMAP constraint by one order of magnitude.
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 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. [2]
This is the value currently most quoted by astronomers.
Assumption of strong priors
Calculating 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 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 WMAP data "only" is 13.4±0.3 Gyr (the slightly higher number of 13.7 includes some other data mixed in). This number represents the first accurate "direct" measurement of the age of the universe (other methods typically involve Hubble's law and 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 WMAP) therefore is to use a Bayesian Statistical analysis, which normalizes the results based upon the priors (i.e. the model).[2] This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.[3] [4]
References
- ^ The Age of the Universe with New Accuracy. Retrieved on 2006-12-29.
- ^ a b Spergel, D. N.; et al. (2003). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters". The Astrophysical Journal Supplement Series 148: 175—194. DOI:10.1086/377226.
- ^ Loredo, T. J.. The Promise of Bayesian Inference for Astrophysics (PDF).
- ^ 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 D 14 (5): 775—796. arXiv:astro-ph/0409245.
External links
- Ned Wright's Cosmology Tutorial
- Wright, Edward L. (2 July 2005). Age of the Universe.
- Wayne Hu's cosmological parameter animations
- J. P. Ostriker and P. J. Steinhardt, Cosmic Concordance, arXiv:astro-ph/9505066.
- SEDS page on "Globular Star Clusters"
- Douglas Scott "Independent Age Estimates"
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