where Ψ = H$_{u}$ if R$_{Φ}$ = +1 and Ψ = L if R$_{Φ}$ = − 1. Taking into account of the inflaton superpotential mass term: ( m$_{φ}$/ 2) ΦΦ, and defining X$_{1}$$_{,}$$_{2}$ = ( H$_{u}$ ± Ψ) $_{/}$√$_{2, the}$ renormalizable part of the potential , which is relevant for the inflaton decay into MSSM scalars is given by: where χ denotes the scalar component of X$_{1}$$_{,}$$_{2}$ superfields, and we have only considered the real parts of the inflaton, φ , and χ field. Further note that the cubic interaction term appears with different signs for χ$_{1}$ and χ$_{2}$ , but this is irrelevant during inflaton oscillations. In addition to the terms in Eq. (417), there are also the self- and-cross-couplings, arising from the superpotential and D -terms respectively ( α is a gauge fine structure con- stant). Therefore even in the simplest SUSY set up the scalar potential is more involved than the non-SUSY case given in Eq. (378), which can alter the picture of preheating presented in the literature, see for the detailed discussion in Refs. [122, 123] $^{93}$. The MSSM flat directions have important role to play in SUSY reheating and thermal- ization [122, 123]. Consider a MSSM flat direction, ϕ , with the corresponding superfield denoted by ϕ (only for flat directions we are denoting the superfield and the field with the same notation in this section). Note that since ϕ and X superfields are linear combinations of the MSSM superfields (defined in the earlier subsection after Eq. (416)), and hence are coupled through the MSSM superpotential in Eq. (103). where Σ$_{1}$$_{,}$$_{2}$ are some MSSM superfields such that Σ$_{1}$ = Ψ and Σ$_{2}$ = H$_{u}$ , since ϕ is a non- gauge-singlet. D. MSSM flat directions, reheating and thermalization V ⊃ 1 2 m 2 $_{φ}$φ 2 + g $^{2}$φ$^{2}$χ2 ± 1 √$_{2}$ gm$_{φ}$φχ $^{2}$, (417) V$_{D}$ ⊃ ( g 2 4 ) ( χ 2 1 − χ 2 ) 2 + αχ 2 $_{1}$χ 2 , (418) W ⊃ λ$_{1}$H$_{u}$ϕ Σ$_{1}$ + λ$_{2}$ Ψ ϕ Σ$_{2}$ + ..., (419) 93 A remarkable feature in Eq. (417) is that SUSY naturally relates the strength of cubic φχ 2 and quartic φ $^{2}$χ2 interactions, which is required for complete decay of the inflaton field. One can also include couplings of the inflaton to fermionic partners of χ . Regarding the prospects for fermionic preheating the same conclusions hold as that of a bosonic case. 195