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is the scale factor of the FRW universe. The interesting point is that, n ∝ a − $^{3}$( t ), as well, and hence Γ$_{thr}$ remains constant while H decreases for H ( t ) < m$_{0}$ ∼ O (100) GeV. This implies that Γ$_{thr}$ eventually catches up with the expansion rate, even if it is initially much smaller, and shortly after that the full thermal equilibrium will be achieved. Depending on whether m$_{0}$ > Γ$_{d}$ or m$_{0}$ < Γ$_{d}$, different situations will arise which we discuss separately $^{96}$. 

• m$_{0}$ > Γ$_{d}$: In this case the inflaton decays after the flat direction oscillations start. The inflaton oscillations, which give rise to the equations of state close to non-relativistic matter, dominate the energy density of the universe for H ( t ) > Γ$_{d}$. This implies that a ( t ) ∝ H − 2 / $^{3}$( t ), and | ϕ | is redshifted ∝ H ( t ) in this period. We therefore have, ϕ$_{d}$ ∼ (Γ$_{d}$ /m$_{0}$ ) ϕ$_{0}$ , where ϕ$_{d}$ denotes the amplitude of the flat direction oscillations at the time of the inflaton decay H ( t ) ≃ Γ$_{d}$. By using the total energy density of the plasma; ρ ≈ 3 (Γ$_{d}$ M$_{P}$ ) $^{2}$, and note that | ϕ | and n are both redshifted ∝ a − $^{3}$( t ) for H < Γ$_{d}$, after using Eq. (430), we find that complete thermalization occurs when the Hubble expansion rate is [122] 

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• m$_{0}$ < Γ$_{d}$: In this case the flat direction starts oscillating after the completion of inflaton decay. The universe is dominated by the relativistic inflaton decay products for H ( t ) < Γ$_{d}$, implying that a ( t ) ∝ H ( t ) − 1 / $^{2}$. The number density of particles in the plasma is redshifted ∝ H ( t ) 3 / 2 until H ( t ) = m$_{0}$ ∼ O (100) GeV. Note that n, | ϕ | 2 ∝ a ( t ) − $^{3}$, and hence Γ$_{thr}$ remains constant, for H ( t ) < m$_{0}$ . The reheat plasma then thermalizes when the Hubble expansion rate is [122] 

<img src='content_image/361121.jpg'>

Since the kinetic equilibrium is built through 2 → 2 scattering diagrams as in Fig. (A), which have one interaction vertex less than those in 2 → 3. Therefore the rate for establish- ment of kinetic equilibrium will be Γ$_{kin}$ ∼ α − $^{1}$Γ$_{thr}$ . In SUSY case, the relevant time scales 

