Cosmological models in $f (T, \mathcal{T})$ gravity and the dynamical system analysis

TL;DR

This paper investigates the dynamics of cosmological models in $f(T, \\mathcal{T})$ gravity using dynamical system analysis, exploring stability and critical points to assess the models' viability in describing the universe.

Contribution

It introduces a formalism for matter-coupled $f(T, \\mathcal{T})$ gravity and applies dynamical system techniques to analyze the stability of cosmological solutions.

Findings

Identification of critical points in $f(T, \\mathcal{T})$ models

Graphical analysis of cosmological behaviors

Insights into the viability of specific $f(T, \\mathcal{T})$ functions

Abstract

The study addresses matter-coupled modified gravity, particularly $f (T, \mathcal{T})$ gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of critical points to understand these models' viability better. The dynamical system analysis of the cosmological models in $f(T, \mathcal{T})$ gravity, where $T$ and $\mathcal{T}$ respectively represent the torsion scalar and trace of the energy-momentum tensor has been investigated. It demonstrates how first-order autonomous systems can be treated as cosmological equations and analyzed using standard dynamical system theory techniques. Two forms of the function $f(T,\mathcal{T})$ are considered (i) one with the product of trace and higher order torsion scalar and the other (ii) linear combination of linear trace and squared torsion. By employing this methodology, the research aims to uncover the actual behavior of the Universe. The findings emphasize the graphical representation of these insights, enriching our understanding of cosmological scenarios.