Noether Symmetry Approach for teleparallel-curvature cosmology

TL;DR

This paper employs the Noether Symmetry Approach to determine the form of the $F(R,T)$ gravity function in curvature-teleparallel cosmology, leading to exact solutions and insights into the model's symmetries.

Contribution

It introduces a method to identify the functional form of $F(R,T)$ gravity using symmetries, enabling exact cosmological solutions in teleparallel-curvature models.

Findings

Determined specific forms of $F(R,T)$ consistent with symmetries.

Derived exact cosmological solutions from conserved quantities.

Illustrated models with particular cosmological behaviors.

Abstract

We consider curvature-teleparallel $F(R,T)$ gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar $R$ and the torsion scalar $T$. Using the Noether Symmetry Approach, we show that the functional form of the $F(R, T)$ function, can be determined by the presence of symmetries . Furthermore, we obtain exact solutions through to the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.