Noether Symmetry Approach in Gauss-Bonnet Cosmology

TL;DR

This paper applies the Noether Symmetry Approach to Gauss-Bonnet cosmology, demonstrating how symmetries determine the form of the function F(R, G) and facilitate finding exact solutions with conserved quantities.

Contribution

It introduces a method to identify the functional form of F(R, G) in Gauss-Bonnet cosmology using symmetries, enabling exact solution derivation.

Findings

Determined specific forms of F(R, G) through symmetry analysis.

Found exact cosmological solutions using conserved quantities.

Reduced the dynamical system for easier analysis.

Abstract

We discuss the Noether Symmetry Approach in the framework of Gauss-Bonnet cosmology showing that the functional form of the $F(R, {\cal G})$ function, where $R$ is the Ricci scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant, can be determined by the presence of symmetries. Besides, the method allows to find out exact solutions due to the reduction of cosmological dynamical system and the presence of conserved quantities. Some specific cosmological models are worked out