Preheating and Supergravity

In this talk 1 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. Preheating after Inflation According to the inflationary scenario, the Universe initially expands quasiexponentially in a vacuum-like state without entropy or particles. At the stage of inflation, all energy is contained in a classical slowly moving inflaton field φ. The fundamental Lagrangian L(φ, χ, ψ, Ai, hik, ...) contains the inflaton part with the potential V (φ) and other fields which give subdominant contributions to gravity. The Friedmann equation for the scale factor a(t) and the Klein-Gordon equation for φ(t) determine the evolution of the background fields. In most of the models, soon after the end of inflation, an almost homogeneous inflaton field φ(t) coherently oscillates with a very large amplitude of the order of the Planck mass around the minimum of its potential. This scalar field can be considered as a coherent superposition of inflatons with zero momenta. The amplitude of oscillations gradually 1) Invited talk to be published in the Proceedings of the 8th Canadian Conference on Reneral Relativity and Relativistic Astrophysics, McGill University, June 10-12, 1999 decreases not only because of the expansion of the universe, but also because energy is transferred to particles created by the oscillating field. At this stage we shall recall the rest of the fundamental Lagrangian which includes all the fields interacting with inflaton. These interactions lead to the creation of many ultra-relativistic particles from the inflaton. Gradually, the inflaton field decays and transfers all of its energy non-adiabatically to the created particles. In this scenario all the matter constituting the universe is created from this process of reheating. If the creation of particles is sufficiently slow, the particles would simultaneously interact with each other and come to a state of thermal equilibrium at the reheating temperature Tr. This gradual reheating can be treated with the perturbative theory of particle creation and thermalization. However, typically particle production from coherently oscillating inflatons occurs not in the perturbative regime but in the non-perturbative regime of parametric excitation. Indeed, let us consider a simple toy model of chaotic inflation with the quadratic potential V (φ) = 1 2 mφφ 2 and Lint = −12gφχ describing the interaction between the inflatons and other massless Bose particles χ. The quantum scalar field χ̂ in a flat FRW background has the eigenfunctions χk(t) e −ikx with comoving momentum k. The temporal part of the eigenfunction obeys the equation