We consider low scale slow roll inflation driven by the gauge invariant flat directions udd and LLe of the Minimally Supersymmetric Standard Model at the vicinity of a saddle point of the scalar potential. We study the stability of saddle point and the slow roll regime by considering radiative and supergravity corrections.The latter are found to be harmless, but the former require a modest finetuning of the saddle point condition. We show that while the inflaton decays almost instantly, full thermalization occurs late, typically at a temperature T ≈ 10 7 GeV, so that there is no gravitino problem. We also compute the renormalization group running of the inflaton mass and relate it to slepton masses that may be within the reach of LHC and could be precisely determined in a future Linear Collider experiment.

We consider a two-field model for inflation where the second order metric perturbations can be amplified by a parametric resonance during preheating. We demonstrate that there can arise a considerable enhancement of non-Gaussianity sourced by the local terms generated through the coupled perturbations. We argue that the non-Gaussianity parameter could be as large as fNL ≈ 50. Our results may provide a useful test of preheating in future CMB experiments.

We discuss gravitino production from reheating in models where the splitting between particle and sparticle masses can be larger than TeV, as naturally arising in the context of split supersymmetry. We show that such a production typically dominates over thermal contributions arising from the interactions of gauginos, squarks and sleptons. We constrain the supersymmetry breaking scale of the relevant sector for a given reheat temperature. However the situation changes when the gravitinos dominate the Universe and decay before nucleosynthesis. We briefly describe prospects for a successful baryogenesis and a viable neutralino dark matter in this case.