Age of the universe

The age of the universe, according to the Big Bang theory, is the time elapsed between the Big Bang and the present day. The current scientific consensus holds this to be about 14.-something billion years.

Explanation

The most conservative (and widely agreed upon) model of the universe has time beginning at the Big Bang, and does not speculate about what may have existed "before" (or even whether this question makes sense). However there are alternative possibilities. In some cosmological models (such as steady state theory or static universe) there is no Big Bang, and the universe has infinite age: however, the current scientific consensus is that the observational evidence overwhelmingly supports the occurrence of a Big Bang. There are also cosmological models (such as the cyclic model) in which the universe has existed forever but has undergone a repeated series of Big Bangs and Big Crunches. In this context, the age of the universe described in this article would be equivalent to the time since the last Big Bang.

There is always an ambiguity in both special and general relativity in defining precisely what is meant by the time between two events. In general, the proper time measured by a clock depends on its state of motion. In the FRW metric generally taken to describe the universe, the preferred measure of time is the time coordinate $t$ appearing in the standard form of the metric. This is also the proper time of a comoving observer (see comoving distance for an intrinsic explanation of the concept).

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, 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.

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.

This is the value currently most quoted by astronomers.

Age as a function of cosmological parameters

File:Universes.GIF

The age of the universe can be determined by measuring the Hubble constant today and extrapolating back in time with the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter dominated and so Ω on this graph corresponds to $\Omega _{m}$. Note that the accelerating universe has the greatest age while the Big Crunch universe has the smallest age.

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 $\Omega _{m}$, $\Omega _{r}$, and $\Omega _{\Lambda }$. The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter $H_{0}$ are the most important.

The value of the age correction factor $F$ is shown as a function of two cosmological parameters: the current fractional matter density $\Omega _{m}$ and cosmological constant density $\Omega _{\Lambda }$. The best-fit values of these parameters is shown by the box in the upper left; the matter-dominated universe is shown by the star in the lower-right.

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,

$t_{0}={\frac {1}{H_{0}}}F(\Omega _{r},\Omega _{m},\Omega _{\Lambda },\dots )$

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,

${\frac {1}{H_{0}}}=\left({\frac {H_{0}}{72\quad {\text{km/(s}}\cdot {\text{Mpc)}}}}\right)^{-1}\times 13.6\quad {\text{Gyr}}$

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 ($\Omega _{m}$,$\Omega _{\Lambda }$) = (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, $\Omega _{r}$ 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.

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 $\Omega _{m}$ [1] and curvature parameter $\Omega _{k}$ [2]. It is not as sensitive to $\Omega _{\Lambda }$ directly [3], partly because the cosmological constant only becomes important at low redshift. The most accurate determinations of the Hubble parameter $H_{0}$ come from type SNIa 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 CNO cycle

Some recent highly controversial studies found the carbon-nitrogen-oxygen cycle to be two times slower than previously believed, leading to the conclusion that (via the CNO cycle) the Universe could be about one billion years older (roughly 15 billion years old) than previous estimates.

Assumption of strong priors

Calculating the age of the universe is only accurate if the assumptions built into the models being used 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 totally invalid procedure in certain contexts, it should be noted that the caveat, "based on the fact we have assumed the underlying model we used is correct", then 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). This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.

External links

• Ned Wright's Cosmology Tutorial
• Wright, Edward L. (2 July 2005). "Age of the Universe". {{cite web}}: Check date values in: |date= (help)
• 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"