Massless Fermions in anisotropic Bianchi type I spacetimes

TL;DR

This paper investigates the behavior of massless spin-1/2 particles in anisotropic Bianchi type I spacetimes, deriving an analytical solution for their evolution using differential forms and Bessel functions.

Contribution

It provides an analytical solution for massless fermions in anisotropic Bianchi I backgrounds with power-law scale factors, extending previous studies to this specific spacetime.

Findings

Analytical expression for the evolution operator in terms of Bessel functions.

Specialization to cases with equal power-law exponents in two directions.

Insights into fermion behavior in anisotropic cosmological models.

Abstract

The behavior of spin - 1/2 - particles in anisotropic Bianchi type I backgrounds is investigated utilizing the concept of differential forms and orthonormal frames. Specializing to the massless case and power law scale factors $\alpha_j(t) = t^{q_j}$ of the metric where $q_1 = q_2 $, an analytical outcome for the time evolution operator in terms of Bessel functions is presented.