Geodesic Deviation Equation in Bianchi Cosmologies

TL;DR

This paper derives and compares the Geodesic Deviation Equation for FRW and Bianchi type I cosmologies, highlighting the anisotropic features of Bianchi models and their significance as alternative cosmological models.

Contribution

It provides the GDE formulation for Bianchi type I models and discusses their differences from FRW models, emphasizing anisotropy and Weyl tensor effects.

Findings

GDE for Bianchi I models derived and analyzed.

Differences between FRW and Bianchi I GDE highlighted.

Bianchi models' anisotropy linked to non-zero Weyl tensor.

Abstract

We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson-Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor in the GDE.