f(G) Noether cosmology

TL;DR

This paper explores $f( ext{Gauss-Bonnet})$ gravity in higher dimensions, identifying power-law models via Noether symmetry, recovering General Relativity, and addressing cosmological phenomena like inflation and dark energy.

Contribution

It introduces a Noether symmetry-based method to select $f( ext{Gauss-Bonnet})$ models, including the case reproducing Einstein gravity and extends to quantum cosmology.

Findings

Power-law $f( ext{G})$ models identified using Noether symmetry.

Reproduction of Einstein gravity without the Einstein-Hilbert action.

De Sitter solutions suggest applications to inflation and dark energy.

Abstract

We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq \mathcal{G}^k$ power-law models where $k$ is a real number. In particular, the case $k = 1/2$ for $n=4$ results equivalent to General Relativity showing that we do not need to impose the action $R+f(\mathcal{G})$ to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $f(\mathcal{G})$ is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.