119 As we are considering the time of the end of primordial inflation, | m$_{φ,}$$_{eff}$ | ∼ g T$_{end,inf}$ , as given by Eq. (4.99). Therefore we have So, we now have where A is a constant of integration. We can obtain A by equating Eq. (A.30) with Eq. (A.14) and setting κ = τ =0 . We obtain Given that | m$_{φ,}$$_{eff}$ | ∼ g T$_{end,inf}$ , we have κ = g . Therefore Eq. (A.30) becomes For all values of g , i.e. g ≤ 1 , we have J (1) − ≃ π 2 3 − πg − 1 2 g $^{2}$ln ( g 4 π ) − 1 2 C g $^{2}$+ 1 4 g 2 (A.33) J (1) − ∼ π 2 3 (A.34) T$_{end,inf}$ ≫ gT$_{end,inf}$ (A.28) g ≪ 1 (A.29) J (1) − ≃ − 1 2 Cκ $^{2}$+ 1 4 κ 2 − 1 2 κ $^{2}$ln ( κ 4 π ) − πκ + A (A.30) A = 2 ∫ ∞ 0 x e x − 1 d x (A.31) = π 2 3 (A.32)