Construction of cosmologically viable f(G) gravity models

TL;DR

This paper establishes conditions for the viability of f(G) gravity models in cosmology, ensuring stability and realistic cosmic evolution, and introduces methods to handle numerical challenges in modeling these theories.

Contribution

It derives stability conditions for f(G) models, presents explicit models with realistic cosmic histories, and introduces an iterative method to improve numerical stability.

Findings

f_GG must be positive for stability and realistic cosmic epochs

Dark energy can cross the phantom divide in these models

An iterative method helps avoid numerical instabilities in simulations

Abstract

We derive conditions under which f(G) gravity models, whose Lagrangian densities f are written in terms of a Gauss-Bonnet term G, are cosmologically viable. The most crucial condition to be satisfied is that f_GG, the second derivative of f with respect to G, must be positive, which is required to ensure the stability of a late-time de-Sitter solution as well as the existence of standard radiation/matter dominated epochs. We present a number of explicit f(G) models in which a cosmic acceleration is followed by the matter era. We find that the equation of state of dark energy can cross the phantom divide before reaching the present Universe. The viable models have asymptotic behavior f_GG goes to +0 when |G| goes to infinity, in which case a rapid oscillation of perturbations occurs unless such an oscillating degree of freedom is suppressed relative to a homogeneous mode in the early universe. We also introduce an iterative method to avoid numerical instabilities associated with a large mass of the oscillating mode.