Self-similar cosmological solutions in f(R,T) gravity theory

TL;DR

This paper investigates self-similar solutions in $f(R,T)$ gravity, deriving exact forms of functions that admit such solutions and generating new cosmological models with concrete examples.

Contribution

It provides a systematic method to find exact self-similar solutions in $f(R,T)$ gravity for two specific models, expanding the understanding of cosmological scenarios.

Findings

Derived general theorems for self-similar solutions in $f(R,T)$ gravity.

Identified exact forms of $f(R,T)$ functions admitting self-similarity.

Generated new cosmological models with explicit solutions.

Abstract

We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the Field Equations (FE) admit exact self-similar solutions through the matter collineation approach. We study two models: the case$\ f(R,T)=f_{1}(R)+f_{2}(T)$ and the case $f(R,T)=f_{1}(R)+f_{2} (R)f_{3}(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_{i}$ such that the field equations admit self-similar solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous self-similar metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.