Noether Symmetries and Some Exact Solutions in $f(R, T^{2})$ Theory

TL;DR

This paper uses Noether symmetry techniques to find exact solutions in a modified gravity theory, demonstrating its potential to model the universe's accelerated expansion consistent with observations.

Contribution

It introduces the application of Noether symmetry to $f(R, T^{2})$ gravity, deriving exact solutions and analyzing their cosmological implications.

Findings

Existence of Noether symmetry generators and conserved quantities in the model.

Derived exact solutions consistent with accelerated cosmic expansion.

Behavior of cosmological quantities aligns with current observational data.

Abstract

The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For this purpose, we assume a generalized anisotropic and homogenous spacetime that yields distinct cosmic models. In order to investigate Noether equations, symmetry generators and conserved quantities, we use a specific model of this modified theory. We find exact solutions and examine the behavior of various cosmological quantities. It is found the behavior these quantities is consistent with current observations indicating that this theory describes the cosmic accelerated expansion. We conclude that generators of Noether symmetry and conserved quantities exist in this theory.