The inhomogeneous reheating scenario with low scale inflation and/or minimal supersymmetric standard model at directions

We discuss the constraints on the inhomogeneous reheating scenario. In particular, we discuss the prospects for low scale inflation with a Hubble constant of the order of the gravitino mass, and the possibility that an MSSM. at direction is responsible for the density fluctuations. Thermal effects are generically fatal for the scenario, and can only be avoided for small enough mass and couplings of the. at direction field, excluding MSSM. at directions. Prompt decay at the end of inflation bypasses thermal constraints, and is compatible with both low scale inflation and MSSM. at directions. However, the level of non-Gaussianity is acceptably small only for a small window of inflaton mass and couplings. The upshot is that tuning of parameters is needed for the inhomogeneous reheating scenario to work.