2.1 General Relativity 9 We can rearrange Eq. (2.11) slightly so that all four spacetime coordinates have the same scale factor, by defining a Conformal Time variable The line element now becomes Let us now assume that the content of the Universe is analogous to a perfect fluid , which is a fluid that has no shear stress, no viscosity and which does not conduct heat. It can be described entirely by its energy density ρ and its isotropic pressure P . In the local rest frame, the Energy- Momentum tensor becomes simply We have not yet employed GR in the discussion regarding our FLRW Universe. All we have assumed so far is a uniformly expanding/contracting homogeneous and isotropic Universe, which has a content that can be de- scribed as a perfect fluid. We now take the “00” (“ tt ”) component of the T$_{µν}$ =    $^{ρ}$ 0 0 0 0 P 0 0 0 0 P 0 0 0 0 P     ds 2 = a $^{2}$( η ) ( − dη 2 + dx 2 + dy 2 + dz 2 ) (2.13) dη = dt a (2.12)