Fermion Propagator in Cosmological Spaces with Constant Deceleration

TL;DR

This paper derives the fermion propagator in cosmological spacetimes with constant deceleration, considering excited states and non-vacuum conditions, enabling analysis of fermionic backreaction on the universe's evolution.

Contribution

It provides a detailed calculation of the fermion propagator in FLRW spaces with constant deceleration, including excited states and non-vacuum conditions, and applies it to study backreaction effects.

Findings

Derived fermion propagator in FLRW with constant deceleration

Normalized spinors via canonical quantization and orthogonality

Calculated one-loop effective action and performed renormalization

Abstract

We calculate the fermion propagator in FLRW spacetimes with constant deceleration $q=\epsilon-1$, $\epsilon=-\dot{H}/H^{2}$ for excited states. For fermions whose mass is generated by a scalar field through a Yukawa coupling $m=g_{\mathrm{\scriptscriptstyle{Y}}} \phi$, we assume $\phi \propto H$. We first solve for the mode functions by splitting the spinor into a direct product of helicity and chirality spinors. We also allow for non-vacuum states. We normalise the spinors using a consistent canonical quantisation and by requiring orthogonality of particle and anti-particle spinors. We apply our propagator to calculate the one loop effective action and renormalise using dimensional regularisation. Since the Hubble parameter is now treated dynamically, this paves the way to study the dynamical backreaction of fermions on the background spacetime.