In the cosmological context, we will describe the universe by a Friedmann–Lemaître spacetime with metric

where is the cosmic time, the scale factor and the metric on the constant time hypersurfaces. The Hubble function is defined as . We also define the redshift by the relation , with the scale factor evaluated today.The evolution of the scale factor is dictated by the Friedmann equation

where is the total energy density of the matter components in the universe. Assuming the species has a constant equation of state , each component evolves as . The Friedmann equation can then be rewritten as with the density parameters defined by They clearly satisfy .Concerning the properties of the cosmological spacetime, I follow the notations and results of [409].

Living Rev. Relativity 14, (2011), 2
http://www.livingreviews.org/lrr-2011-2 |
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