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## E. Quasi-adiabatic thermal evolution of the universe 

Before complete thermalization is reached the universe remains out of equilibrium $^{100}$.The deviation from full equilibrium can be quantified by the parameter $^{′′}$A′′ [122, 749], where 

Here we define T ≈ 〈 E 〉 / 3, in accordance with full equilibrium. Note that in full equilibrium, see Eq. (375), we have A ≈ $^{g}$∗ (= 228 . 75 in the MSSM). 4 

One can also associate parameter A i ≡ 3 ρ$_{i}$/T to the i − th degree of freedom with the energy density ρ$_{i}$ (all particles have the same energy E , and hence T , as they are produced in one-particle decay of the inflaton). Note that A = ∑ i A $_{i}$, and in full equilibrium we have A i ≃ 1. Note that A depends on the total decay rate of the inflaton Γ$_{d}$ and its mass m$_{φ}$ through Eq. (435). While, A i are determined by the branching ratio for the inflaton 

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