Spin 1/2 field and regularization in de Sitter and radiation dominated universe

TL;DR

This paper develops an adiabatic regularization method for calculating spin 1/2 particle creation and energy-momentum tensor in curved spacetimes, extending techniques from scalar fields to fermions, and applies it to cosmological models.

Contribution

It introduces a simple algorithm for fermionic particle creation in curved spacetime, extending existing scalar field techniques to spin 1/2 fields in FLRW universes.

Findings

Consistent particle number density results with known literature

Effective analytical and numerical computation in de Sitter and radiation universes

Demonstrates the efficiency of the proposed regularization method

Abstract

We construct a simple algorithm to derive number density of spin 1/2 particles created in spatially flat FLRW spacetimes and resulting renormalized energy-momentum tensor within the framework of adiabatic regularization. Physical quantities thus found are in agreement with the known results. This formalism can be considered as an appropriate extension of the techniques originally introduced for scalar fields, applicable to fermions in curved space. We apply this formalism to compute the particle number density and the renormalized energy density and pressure analytically (wherever possible) and numerically, in two interesting cosmological scenarios: a de Sitter spacetime and a radiation dominated universe. Results prove the efficiency of the methodology presented here.