2.1 General Relativity 12 The physical interpretation of the extra “ a ” factor compared to the case of matter is that the frequency of the radiation is red-shifted as the Universe expands, hence it loses energy. In the case of K = 0 (i.e. our Universe), the Friedmann equation yields the solution for the evolution of the scale factor as for w> − 1 and constant. Therefore, for matter domination we have and for radiation domination we have In the case of a cosmological constant (see Section 2.3) (and also for inflation (see Section 3.2.2)), which is causing the expansion of the Universe to accelerate, beginning from around the time of the current epoch, the equation of state is w = − 1. For this situation, Eq. (2.24) is not valid. Instead, Eqs. (2.19) and (2.21) give that ˙ ρ = 0 (c.f. Eq. (2.18)). H ≡ ˙ a a is constant and the evolution of the scale factor is a ( t ) ∝ e Ht (2.27) a ( t ) ∝ t 1 2 (2.26) a ( t ) ∝ t 2 3 (2.25) a ( t ) ∝ t 2 3( w +1) (2.24)