Light propagation in a homogeneous and anisotropic universe

TL;DR

This paper provides a detailed analytical study of light propagation in a homogeneous, anisotropic Bianchi I universe, deriving key optical quantities and extending previous formulas to include shear and rotation effects.

Contribution

It offers explicit expressions for redshift, direction drifts, and the Jacobi matrix in Bianchi I spacetime, enhancing understanding of light behavior in anisotropic cosmologies.

Findings

Derived analytical expressions for redshift and direction drifts.

Obtained explicit Jacobi matrix including shear and rotation.

Recovered and extended Saunders' angular diameter distance formula.

Abstract

This article proposes a comprehensive analysis of light propagation in an anisotropic and spatially homogeneous Bianchi I universe. After recalling that null geodesics are easily determined in such a spacetime, we derive the expressions of the redshift and direction drifts of light sources; by solving analytically the Sachs equation, we then obtain an explicit expression of the Jacobi matrix describing the propagation of narrow light beams. As a byproduct, we recover the old formula by Saunders for the angular diameter distance in a Bianchi I spacetime, but our derivation goes further since it also provides the optical shear and rotation. These results pave the way to the analysis of both supernovae data and weak lensing by the large-scale structure in Bianchi universes.