Dynamical systems analysis in $f(T,\phi)$ gravity

TL;DR

This paper applies dynamical systems analysis to $f(T,)$ gravity models, exploring their cosmological behavior, stability, and phases such as matter, radiation, and dark energy, through critical points and graphical representations.

Contribution

It introduces a dynamical system approach to analyze $f(T,)$ gravity models, identifying critical points and their stability, and illustrating cosmological phases with specific functional forms.

Findings

Critical points correspond to different cosmological phases.

Stability analysis reveals conditions for matter, radiation, and dark energy dominance.

Graphical results illustrate the evolution of the equation of state and density parameters.

Abstract

Teleparallel based cosmological models provide a description of gravity in which torsion is the mediator of gravitation. Several extensions have been made within the so-called Teleparallel equivalent of general relativity which is equivalent to general relativity at the level of the equations of motion where attempts are made to study the extensions of this form of gravity and to describe more general functions of the torsion scalar $T$. One of these extensions is $f(T,\phi)$ gravity; $T$ and $\phi$ respectively denote the torsion scalar and scalar field. In this work, the dynamical system analysis has been performed for this class of theories to obtain the cosmological behaviour of a number of models. Two models are presented here with some functional form of the torsion scalar and the critical points are obtained. For each critical point, the stability behaviour and the corresponding cosmology are shown. Through the graphical representation the equation of state parameter and the density parameters for matter-dominated, radiation-dominated and dark energy phase are also presented for both the models.