A Dynamical System Analysis of $f(R,T)$ Gravity

TL;DR

This paper analyzes the dynamical behavior and potential future singularities in $f(R,T)$ gravity, exploring fixed points, symmetries, and the impact of different equations of state on the theory's evolution.

Contribution

It introduces a dynamical systems approach to $f(R,T)$ gravity, identifies fixed points, and determines the form of $f(R,T)$ consistent with Noether symmetry.

Findings

No future singularity for barotropic perfect fluid

Possible future singularities with generalized equations of state

Determined $f(R,T)$ form using Noether symmetry

Abstract

We investigate equations of motion and future singularities of $f(R,T)$ gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate $f(R,T)$ gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on $f(R,T)$ is studied and the consistent form of $f(R,T)$ function is found using the symmetry and the conserved charge.