Growth factor in $f(T,\mathcal{T})$ gravity

TL;DR

This paper studies the growth of matter perturbations during late times in $f(T, ext{T})$ gravity by deriving a modified Mészáros equation and analyzing the effects of anisotropic stress, providing numerical insights into structure formation.

Contribution

It introduces a modified Mészáros equation for $f(T, ext{T})$ gravity and explores the impact of anisotropic stress on matter perturbation growth.

Findings

Numerical solutions show the behavior of matter density perturbations.

Anisotropic stress influences the growth rate of structures.

Constraints on integration constants affect perturbation evolution.

Abstract

We investigate the growth factor for sub-horizon modes during late times in $f(T,\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\mathcal{T}$ is the trace of the stress-energy tensor. This is achieved by obtaining the modified M\'{e}sz\'{a}ros equation, which describes the evolution of the perturbations of the matter energy density, and obtaining numerical results. Such results are obtained by solving the modified continuity equation and analysing the behaviour of the solutions of the latter using various constraints on the integration constants. Furthermore, the role of the anisotropic term $\pi^{S}$ is investigated.