Dynamical System Analysis for Scalar Field Potential in Teleparallel Gravity

TL;DR

This paper investigates the dynamics of scalar fields in teleparallel gravity using a power law cosmological model, analyzing critical points and their stability to understand the universe's evolution.

Contribution

It introduces a dynamical system analysis for $f(T,)$ gravity with specific coupling functions and potentials, providing new insights into cosmological evolution.

Findings

Critical points correspond to different cosmic epochs.

Model parameters are constrained by stability conditions.

Results align with cosmological observations.

Abstract

In this paper, we have presented a power law cosmological model and its dynamical system analysis in $f(T,\phi)$ gravity, where $T$ is the torsion scalar and $\phi$ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $F(\phi)$, the exponential form and the power law form, with exponential potential function, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter show agreement with the result of cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.