Preheating and supergravity

In this talk recent developments of the theory of preheating after inflation are briefly reviewed. In inflationary cosmology, the particles constituting the Universe are created after inflation due to their interaction with moving inflaton field(s) in the process of reheating. In inflationary models motivated by supergravity, both bosons and fermions are created. In the bosonic sector, the leading channel of particle production is the non-perturbative regime of parametric resonance dominated by those bosons which are created exponentially fast with the largest characteristic exponent. In the fermionic sector, the leading channel corresponds to the regime of parametric excitation of fermions, which respects Pauli blocking but differs significantly from the perturbative expectation. In supergravity we also have to consider production of gravitinos and moduli fields, which are cosmologically dangerous relics. We discuss the derivation of the gravitino equations in curved space-time with moving background scalars. We describe recent results on the production of gravitinos from preheating, which may put strong constraints on the inflationary models.