Higher-Order Gauss-Bonnet Cosmology

TL;DR

This paper explores cosmological models based on higher-order Gauss-Bonnet gravity, analyzing the effects of Lagrange multipliers and compatibility conditions on solutions without extra fields.

Contribution

It introduces a Lagrange multiplier approach to higher-order Gauss-Bonnet gravity, revealing restrictions on solutions and the need for exotic matter or specific metric conditions.

Findings

Lagrange multipliers limit the solution space

Compatibility conditions impose strict restrictions

Several classes of models are generated and discussed

Abstract

We study cosmological models derived from higher-order Gauss-Bonnet gravity $F(R,G)$ by using the Lagrange multiplier approach without assuming the presence of additional fields with the exception of standard perfect fluid matter. The presence of Lagrange multipliers reduces the number of allowed solutions. We need to introduce compatibility conditions of the FRW equations, which impose strict restrictions on the metric or require the introduction of additional exotic matter. Several classes of $F(R,G)$ models are generated and discussed.