# age of the Universe

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## age of the Universe

The observed expansion and evolution of the Universe suggest that it has a finite age, considered as the time since the Big Bang. The inverse Hubble constant, 1/*H*

_{0}, gives a measure of the age if the rate of expansion has always been constant. Since gravitation tends to diminish the expansion rate,

*H*

_{0}can only give an upper limit. Using the value of

*H*

_{0}of 75 km s

^{–1}Mpc

^{–1}gives an upper limit of 13 billion (10

^{9}) years.

In the standard cosmology (solutions of Einstein's field equations without a cosmological constant) with deceleration parameter *q *_{0}, the age is given as one of the three alternatives:

*H*

_{0}

^{–1}

*q*

_{0}(2

*q*

_{0}– 1)

^{–3/2}[cos

^{–1}(

*q*

_{0}

^{–1}– 1) –

*q*

_{0}

^{–1}(2

*q*

_{0}– 1)

^{½}]

*H*

_{0}

^{–1}

*H*

_{0}

^{–1}

*q*

_{0}(1 – 2

*q*

_{0})

^{–3/2}[

*q*

_{0}

^{–1}(1 – 2

*q*

_{0})

^{½}– cosh

^{–1}(

*q*

_{0}

^{–1}– 1)]

The choice depends on whether *q *_{0} exceeds, equals, or is less than ½ (and > 0), i.e. on whether the Universe is closed, flat, or open, respectively. Ages of 12 and 15 × 10^{9} years thus correspond to values of *q *_{0} of ½ and 0.15, for *H *_{0} equal to 55 km s^{–1} Mpc^{–1}.

Lower limits to the age of the Universe, other than through measurements of *H *_{0} and *q *_{0}, can be found from radiometric dating of the Earth and Galaxy and from studies of globular clusters. For example, the relative abundances of radioactive elements, such as uranium, and their decay products yield an estimate of the time since formation of that body of material e.g., the Earth. The results give an age for the Universe of 14–16 × 10^{9} years. The age of a globular cluster may be estimated by comparison of the observed main-sequence turnoff point in the Hertzsprung–Russell diagram for the cluster with theoretical models. The oldest globular clusters in our Galaxy then work out to be 14–18 × 10^{9} years old. Both of these ages should be less than the age of the Universe and in particular they must be less than *H *_{0} ^{–1}. If the expansion of the Universe is now accelerating due to a cosmological constant, then the Universe will be slightly older than given by the above estimates.