As a consequence the two-body inflaton decay via the superpotential term; Φ H$_{u}$H$_{d}$ term will be kinematically forbidden, but Φ H$_{u}$L term will led to the inflaton decay into MSSM degrees of freedom. The VEV of udd direction keeps SU (2)$_{W}$ unbroken, so that the decay products of the inflaton with SU (2)$_{W}$ degrees of freedom can completely thermalize before the curvaton, udd , has a chance to dominate and decay. • QLd : This monomial represents a subspace of complex dimension 19 [407]. F -flatness requires that Q and d belong to different generations. Then, since Q and d are both coupled to H$_{d}$ , Eq. (447) implies that λ$_{2}$ ≥ 10 − $^{3}$. The two-body inflaton decay via superpotential Φ H$_{u}$H$_{d}$ term will be kinematically forbidden, but the other superpoten- tial term is kinematically allowed, i.e. Φ H$_{u}$L . The VEV of QLd directions completely break the SU (2)$_{W}$ × U (1)$_{Y}$, but leave a SU (2) subgroup of the SU (3)$_{C}$ unbroken. Therefore the associated color degrees of freedom can thermalize quickly to SM de- grees of freedom, before QLd could dominate the energy density. • LLe This monomial represents a subspace of complex dimension three [407]. D - flatness requires that the two L s are from different generations, while F -flatness re- quires that e belongs to the third generations (therefore all the three lepton generations will be involved). A feasible curvaton candidate will be L$_{2}$L$_{3}$e$_{1}$ direction. For this flat direction we have λ$_{1}$ = 0 and λ$_{3}$ ∼ 10 − 5 (see Eq. (447)). This implies that two-body inflaton decay will proceed via the Φ H$_{u}$L$_{1}$ term without trouble. The flat direction VEV breaks the electroweak symmetry SU (2)$_{W}$ × U (1)$_{Y}$, while not affecting SU (3)$_{C}$. • LLddd : This monomial represents a subspace of complex dimension three [407]. D - flatness requires that the two L s and the three d s are all from different generations. This implies that that λ$_{2}$ ≃ 10 − 2 and λ$_{1}$ = λ$_{3}$ = 0 (see Eq. (447)). This direction breaks all of the SM gauge group. This results in late thermalization of the Uni- verse [122, 749] and the absence of thermal effects which, as a consequence, does not yield early oscillations of the flat direction. Thus within MSSM the potential curvaton candidates could be the u$_{1}$d$_{2}$d$_{3}$ and Q$_{1}$L$_{3}$d$_{2}$ (and possibly L$_{2}$L$_{3}$e$_{1}$ ) flat directions. Because in all these two cases the inflaton can decay and produce a thermal bath, which will enable the curvaton oscillations to dominate early during its oscillations, and the curvaton can receive finite temperature thermal corrections. 213