Age of the universe

Physical cosmology
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The age of the Universe, according to the Big Bang theory, is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch back to the "Big Bang". The time that has elapsed on a hypothetical clock which has existed since the Big Bang and is now here on Earth will depend on the motion of the clock. According to the preceding definition, the age of the universe is just the largest possible value of time having elapsed on such a clock.

Some have postulated that the universe has always existed, so there is no "beginning" of the universe (such as Steady state theory (later reformulated into the Quasi-steady state theory) and the Plasma universe theory). Various creationist cosmologies have dated creation of the universe at a much different scale. Below is a discussion of the age of the universe according to the Big Bang theory.

Age based on WMAP

NASA's Wilkinson Microwave Anisotropy Probe (WMAP) project estimates the age of the universe to be:

\left( 13.7 \plusmn 0.2 \right) \times 10^{9} \ \mathbf{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 pretty good 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.

Age based on CNO cycle

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

Planck units

There is a simplification where if expressed in Planck units, the age (to/tp) is equal to the inverse square of the temperature (To/Tp) of the universe. Dividing To/Tp gives the current temperature expressed in the amount of the Planck temperature 6 \times 10^{-31}. Taking the inverse square gives 2.72 \times 10^{60} which is the age in Planck units. Multiplying by the Planck time gives the 11.667 Gyr again. There are many other simple relations like this one, including the critical density as the Planck temperature raised to the fourth power. In Planck units, the critical density is 1.3 \times 10^{-121}, which when multiplied by the Planck density gives 3.3 \times 10^{-30} g/cm3.

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.