Couple of points to note here. In the borderline regime σ ∼ h $^{2}$M$_{P}$ , the cubic and quartic interaction terms are comparable. The inflaton decay happens due to a combination of resonant and tachyonic instabilities. If h ≪ m$_{φ}$/M$_{P}$ and σ ≪ m 2 $_{φ}$/M$_{P}$ , the inflaton decays perturbatively via the cubic interaction term. However this requires very small couplings; h, ( σ/m$_{φ}$ ) < 10 − $^{6}$. Therefore, unless the inflaton is only gravitationally coupled to other fields, the initial stage of its decay will be generically non-perturbative. Resonant particle production and re-scatterings lead to the formation of a plasma con- sisting of φ and χ quanta with typical energies ∼ 10 − $^{1}$( hm$_{φ}$M$_{P}$ ) 1 / $^{2}$, see [100, 115, 725, 796]. This plasma is in kinetic equilibrium but full thermal equilibrium is established over a much longer time scale than preheating [102, 104]. The occupation number of particles in the preheat plasma is ≫ 1 (which is opposite to the situation after the perturbative decay). This implies that the number density of particles is larger than its value in full equilibrium, while the average energy of particles is smaller than the equilibrium value. It gives rise to large effective masses for particles which, right after preheating, is similar to their typical momenta [100, 115, 796]. Large occupation numbers also lead to important quantum effects due to identical particles and significant off-shell effects in the preheat plasma. Because of all these, a field theoretical study of thermalization is considerably more complicated in case of preheating. Due to the large occupation numbers, one can consider the problem as thermalization of classical fields at early stages [101–104]. In the course of evolution towards full equilibrium, however, the occupation numbers decrease. Therefore a proper (non-equilibrium) quantum field theory treatment will be inevitably required at late stages when occupation numbers are close to one. Preheating ends due to back reaction as well as the expansion of the universe. Preheating does not destroy the zero mode of the inflaton condensate completely, although the amplitude of the inflaton oscillations diminish, but the inflaton decay is completed when the zero mode perturbatively decays into the SM or some other degrees of freedom, see [97–100]. It was found that the relevant time scale for thermalization after preheating is given by [101, 102]: where c$_{r}$ is the fraction of the inflaton energy density stored in the coherent oscillations at the onset of the turbulent phase and p ∼ 1 / 7 obtained from the numerical simulations. 179 Γ$_{th}$ ∼ ( m$_{φ}$ ( c$_{r}$ρ$_{inf}$ ) 1 / 4 ) 1 /p , (382)