Supersymmetric inflation and baryogenesis via Extra-Flat directions of   the MSSM
  One interpretation of proton stability is the existence of extra-flat directions of the MSSM, in particular $u^{c}u^{c}d^{c}e^{c}$ and $QQQL$, where the operators lifting the potential are suppressed by a mass scale $\Lambda$ which is much larger than the Planck mass, $ \Lambda \gae 10^{26} \GeV$. Using D-term hybrid inflation as an example, we show that such flat directions can serve as the inflaton in SUSY inflation models. The resulting model is a minimal version of D-term inflation which requires the smallest number of additional fields. In the case where $Q$-balls form from the extra-flat direction condensate after inflation, successful Affleck-Dine baryogenesis is possible if the suppression mass scale is $\gae 10^{31}-10^{35} \GeV$. In this case the reheating temperature from $Q$-ball decay is in the range $3-100 \GeV$, while observable baryon isocurvature perturbations and non-thermal dark matter are possible. In the case of extra-flat directions with a large $t$ squark component, there no $Q$-ball formation and reheating is via conventional condensate decay. In this case the reheating temperature is in the range $1-100 \TeV$, naturally evading thermal gravitino overproduction while allowing sphaleron erasure of any large B-L asymmetry. 
John McDonald and Osamu Seto