Coupled fields in external background with application to nonthermal production of gravitinos

TL;DR

The paper develops a formalism for quantizing coupled bosonic and fermionic fields in a time-dependent background by promoting Bogolyubov coefficients to matrices $\alpha$ and $\beta$, enabling consistent definitions of occupation numbers for the physical eigenstates. It provides parallel treatments for bosons and fermions, deriving first-order evolution equations for $\alpha$ and $\beta$, and establishes normalization conditions that preserve unitarity and the Pauli principle. The framework is then applied to a two-field supergravity model to study non-thermal gravitino production, showing that longitudinal gravitino production is strongly suppressed when the inflation and SUSY-breaking sectors couple weakly and are hierarchically separated. This work clarifies how multi-field couplings and background dynamics control particle production after inflation and has implications for gravitino cosmology in models with decoupled or weakly coupled sectors.

Abstract

We provide the formalism for the quantization of systems of coupled bosonic and fermionic fields in a time dependent classical background. The occupation numbers of the particle eigenstates can be clearly defined and computed, through a generalization of the standard procedure valid for a single field in which Bogolyubov coefficients are employed. We apply our formalism to the problem of nonthermal gravitino production in a two-fields model where supersymmetry is broken gravitationally in the vacuum. Our explicit calculations show that this production is strongly suppressed in the model considered, due to the weak coupling between the sector which drives inflation and the one responsible for supersymmetry breakdown.