flat directions which do not dominate while decaying, they have a possibility to generate large non-Gaussianity, see for example [852, 853], where the imaginary part of the MSSM flat direction curvaton is responsible for generating the perturbations. In these models the treatment for the inflaton decay products is not quite complete, it is not clear in which sector the inflaton decays. Thermal corrections are important for the MSSM flat direction potential as we have seen in the above discussion. There are many viable candidates of curvaton within MSSM which do not use A -term. These are flat directions which are lifted by hybrid operators, such as W ∼ Φ n − $^{1}$Ψ /M n − $^{3}$, for such operators the A -term becomes dynamically negligible. A generic curvaton potential is given by [134, 135, 840, 841]: The flat direction candidate, i.e QuQuQue (lifted by QuQuQuH$_{d}$ee ) by the superpotential term n = 9 is the only viable term which can dominate the energy density of the universe at the time of decay [134, 135]. Note that the superpotential term which lifts the direction is a hybrid type and therefore the A -term vanishes, see the discussion after Eq. (315). In these models, it was assumed that prior to the curvaton domination the inflaton decays primarily into the hidden sector radiation, which is not a satisfactory assumption. For n = 7 the flat direction is LLddd (lifted by H$_{u}$LLLddd ), and for n = 6 the flat direction QdL (lifted by QdLudd ) are allowed to be a curvaton candidate, provided the background equation of state is that of a stiff fluid at the time of curvaton oscillations. The flat directions which are lifted by n = 4 or by n = 3 can never dominate the energy density of the universe. This is due to the fact that their initial amplitude of the oscillations is very low. There is of course a way to cure flat directions which are lifted by n = 4 by the renormal- izable superpotential, such as H$_{u}$H$_{d}$ (lifted by ( H$_{u}$H$_{d}$ ) $^{2}$), and for n = 3, the flat direction NH$_{u}$L , in the extension of the SM gauge group by U $^{(1)$_{B}$}$− $_{L}$, where N is the right handed neutrino. They can dominate the energy density of the universe during oscillations, provided the inflaton energy never gets dumped into the observable world [841]. 218 5. Models without A-term V ( ϕ ) = m 2 $_{0}$ϕ 2 + λ 2 $_{n}$| ϕ | 2( n − 1) M 2( n − 3) P . (458)