Note that the above discussions assume that all the MSSM degrees of freedom are in thermal equilibrium instantly right after inflation, however this basic assumption is in con- tradiction in presence of MSSM flat directions [122], which alters the thermal history of the universe and also affects the gravitino abundance. 

## 2. Gauge singlet inflaton couplings to MSSM 

Within MSSM there exists two gauge-invariant combinations of only two superfields: 

The combinations which include three superfields are: 

H$_{u}$H$_{d}$, H$_{u}$L. (414) 

H$_{u}$Qu, H$_{d}$Qd, H$_{d}$Le, QLd, udd, and LLe. (415) 

SUSY together with gauge symmetry requires that the inflaton (a SM gauge singlet) su- perfield be coupled to these combinations. The superpotential terms Φ H$_{u}$H$_{d}$ and Φ H$_{u}$L have dimension four, and hence are renormalizable. On the other hand, the interaction terms that couple the inflaton to the combinations with three superfields have dimension five and are non-renormalizable. In following we focus on renormalizable interactions of the inflaton with matter which play the dominant role in its decay. Further note that terms representing gauge-invariant coupling of the inflaton to the gauge fields and gauginos are also of dimension five, and hence preheating into them will be suppressed $^{92}$. 

Preserving R -parity at the renormalizable level further constrains inflaton couplings to matter. Note that H$_{u}$H$_{d}$ is assigned +1 under R -parity, while H$_{u}$L has the opposite as- signment − 1. Therefore only one of the couplings preserves R -parity: Φ H$_{u}$H$_{d}$ if R$_{Φ}$ = +1, and Φ H$_{u}$L . If R$_{Φ}$ = − 1 (such as models where the RH sneutrino plays the role of the inflaton [783]). Therefore the renormalizable inflaton coupling to matter can be represented as [123]: 

2 g Φ H$_{u}$ Ψ (416) 

