For example consider the case where ϕ is a flat direction classified by the udd monomial, and Ψ = H$_{d}$ . In this case Σ$_{1}$$_{,}$$_{2}$ are Q superfields and λ$_{1}$$_{,}$$_{2}$ correspond to λ$_{u}$ and λ$_{d}$ respectively. Then with the help of X$_{1}$$_{,}$$_{2}$ = ( H$_{u}$ ± Ψ) $_{/}$√$_{2, part of MSSM superpotential can be written}$ as: W ⊃ λ 1 √$_{2}$ Xϕ Σ$_{1}$ + λ 2 √$_{2}$ Xϕ Σ$_{2}$. This results in [123]: where we have again considered the real part of χ . Note that the first generation of (s)leptons and (s)quarks have a Yukawa coupling ∼ O (10 − 6 − 10 − $^{5}$), while the rest of the SM Yukawa couplings are: λ ≥ 3 × 10 − $^{4}$. The most important point is to note that 60 − 70 e-foldings of inflation is sufficient for the MSSM flat directions to take large VEVs during and after inflation by virtue of stochastic jumps during inflation, see the discussion in Sec. V E 1 and the Refs. [91, 92]. This however requires that the MSSM flat directions do not obtain positive Hubble induced corrections during inflation. 1. kinematical blocking of preheating In order to understand the preheating dynamics it is important to take into account of χ coupling to the inflaton φ , as well as to the MSSM flat direction, ϕ , which is displaced away from its minimum (towards large VEVs) during inflation. The governing potential can be obtained from Eqs. (417,420): As mentioned in the previous section, we generically have λ ≥ 3 × 10 − $^{4}$, and g can be as large as ∼ O (1). After mode decomposition of the field χ , the energy of the mode with momentum k , denoted by χ$_{k}$ , is given by: Let us freeze the expansion of the universe first. Including the expansion will not change our conclusions anyway. Let us even consider the most opportunistic case for preheating with a large inflaton VEV, i.e. 〈 φ 〉 > M$_{P}$ . Therefore if g > 10 − $^{6}$, the inflaton induces a large mass g 〈 φ 〉 > H$_{inf}$ for χ during inflation. As a result, χ , quickly settles down to the minimum, i.e. 196 V ⊃ λ $^{2}$| ϕ | $^{2}$χ 2 , λ ≡ ( λ 2 1 + λ 2 8 ) 1 / 2 , (420) V = 1 2 m 2 $_{φ}$φ 2 + g $^{2}$φ$^{2}$χ2 + g √$_{2}$ m$_{φ}$φχ 2 + λ $^{2}$ϕ$^{2}$χ$^{2}$. (421) ω$_{k}$ = ( k 2 + 2 g $^{2}$〈 φ 〉 2 + √$_{2}$$_{gm}$$_{φ}$ 〈 φ 〉 + 2 λ $^{2}$〈 ϕ 〉 2 ) 1 / $^{2}$. (422)