Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity

TL;DR

This paper applies Noether symmetry methods to $f( ext{Gauss-Bonnet}, T)$ gravity to identify viable models and derive exact solutions, including deSitter spacetime, in a flat FRW universe.

Contribution

It introduces a Noether symmetry approach to $f( ext{Gauss-Bonnet}, T)$ gravity and constructs specific models with conserved quantities and exact solutions.

Findings

Derived Noether equations for flat FRW universe

Identified conserved quantities in specific models

Reconstructed deSitter solutions for certain $f( ext{Gauss-Bonnet}, T)$ models

Abstract

We explore the recently introduced modified Gauss-Bonnet gravity [1], $f(\mathcal{G},T)$ pragmatic with $\mathcal{G}$, the Gauss-Bonnet term, and ${T}$, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable $f(\mathcal{G},T)$ gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of $f(\mathcal{G},T)$ gravity model.