Weyl time evolution operator in planar Bianchi-type-I universes

TL;DR

This paper derives an approximate analytical time evolution operator for massless spinors in anisotropic Bianchi-I universes, enabling the generation of solutions that match exact solutions asymptotically and at early times, with applications to near-conformally flat backgrounds.

Contribution

It introduces an analytical approximate time evolution operator for Dirac spinors in Bianchi-I spacetimes, facilitating solution generation and analysis of anisotropic effects.

Findings

The operator reproduces exact solutions asymptotically and at early times.

It effectively models small deviations from conformally flat backgrounds.

The approach simplifies studying anisotropic cosmological models.

Abstract

In this paper, Dirac`s equation in anisotropic Bianchi-type-I background spacetimes is treated w.r.t. orthonormal frames. By specializing to the massless spinor case and metrics with power-law scale factors and planar symmetry, an analytical expression of the approximate time evolution operator is derived. By use of this operator, all approximate spinor solutions can be generated. By construction, these solutions agree asymptotically and at early times with the exact solutions. The operator approach is also well adapted for studying the case of small deviations from conformally flat backgrounds. In particular, it can be shown that the limiting case of vanishing anisotropy renders the correct