Homothetic Motion in a Bianchi Type-I Model in Lyra Geometry

TL;DR

This paper explores homothetic vector fields in a Bianchi type-I cosmological model within Lyra geometry, comparing results with those from General Relativity to understand geometric effects on cosmological solutions.

Contribution

It introduces a study of homothetic vectors in Bianchi type-I models in Lyra geometry, analyzing cases with variable and constant displacement vectors, and compares with Riemannian geometry results.

Findings

Different behaviors of the equation of state depending on the displacement vector

Comparison highlights differences between Lyra and Riemannian geometries

Results contribute to understanding geometric influences on cosmological models

Abstract

In this paper we study a homothetic vector field of a Bianchi type-I model based on Lyra geometry. The cases when a displacement vector is function of $t$ and when it is constant are considered. In both two cases we investigate the equation of state. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity, based on Riemannian geometry, will be given.