Instantaneous vacuum for Dirac fields with a Yukawa interaction in cosmological space-times

Abstract

We propose a suitable vacuum state for a quantized Dirac field interacting with a classical scalar field in a Friedman-Robertson-Walker-Lemaitre spacetime. This state is constructed from an extended version of the adiabatic expansion of the associated Fourier modes of the field. We compute the full renormalized stress-energy tensor. For any given initial time, this instantaneous vacuum can always be chosen to have vanishing Fourier modes for the renormalized stress-energy tensor. We check the consistency of the solution for several inflationary models.