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

TL;DR

This paper introduces an instantaneous vacuum state for quantized Dirac fields with Yukawa interactions in cosmological spacetimes, enabling consistent stress-energy tensor calculations during inflation.

Contribution

It constructs a new vacuum state based on an extended adiabatic expansion for Dirac fields interacting with scalar fields in FRW spacetimes, and computes the renormalized stress-energy tensor.

Findings

The vacuum state can be chosen to have vanishing stress-energy Fourier modes at any initial time.

The approach is consistent across various inflationary models.

The method facilitates stress-energy tensor calculations in interacting quantum fields in cosmology.

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.