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

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.