The Cosmology of Modified Gauss-Bonnet Gravity

TL;DR

This paper explores how modified Gauss-Bonnet gravity models can explain the universe's late-time acceleration, deriving perturbation equations, analyzing stability constraints, and demonstrating that such models are highly restricted by cosmological data.

Contribution

It derives covariant perturbation equations for f(G) gravity and analyzes stability constraints, showing these models are tightly constrained by cosmological observations.

Findings

f(G) models cannot replicate arbitrary cosmic histories like LCDM without being a true cosmological constant

Stability of perturbations requires d^2f/dG^2 < 0, limiting functional forms of f(G)

Numerical analysis demonstrates strong constraints on f(G) models from cosmological data

Abstract

We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,R^abR_ab,R^abcdR_abcd) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard LCDM paradigm with Omega_DE = 0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case d^2 f/d G^2 < 0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative LCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data.