Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity

TL;DR

This paper extends the geodesic deviation equation within $f(T, T)$ gravity, deriving new relations and numerically solving for null vectors, offering potential observational tests for this modified gravity model.

Contribution

It generalizes the geodesic deviation and Raychaudhuri equations in $f(T, T)$ gravity and provides numerical solutions for null vectors under specific models.

Findings

Derived generalized Raychaudhuri and Mattig relations in $f(T, T)$ gravity.

Numerically solved geodesic deviation for null vectors with specific $f(T, T)$ form.

Results suggest testable predictions with observational data.

Abstract

The geodesic deviation equation has been investigated in the framework of $f(T,\mathcal{T})$ gravity, where $T$ denotes the torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor, respectively. The FRW metric is assumed and the geodesic deviation equation has been established following the General Relativity approach in the first hand and secondly, by a direct method using the modified Friedmann equations. Via fundamental observers and null vector fields with FRW background, we have generalized the Raychaudhuri equation and the Mattig relation in $f(T,\mathcal{T})$ gravity. Furthermore, we have numerically solved the geodesic deviation equation for null vector fields by considering a particular form of $f(T,\mathcal{T})$ which induces interesting results susceptible to be tested with observational data.