MSSM at direction inflation: slow roll, stability fine-tuning and reheating

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 the 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 fine-tuning of the saddle point condition. We show that, while the inflaton decays almost instantly, full thermalization occurs late, typically at a temperature T approximate to 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 the LHC and could be precisely determined in a future linear collider experiment.