Ghost conditions for Gauss-Bonnet cosmologies

TL;DR

This paper analyzes the stability and ghost conditions in Gauss-Bonnet cosmologies with scalar fields, deriving constraints for consistency and testing models for dark energy, revealing many are unstable or observationally unviable.

Contribution

It provides a comprehensive stability analysis of Gauss-Bonnet cosmologies, deriving no-ghost conditions, and evaluates the viability of models for dark energy against observational constraints.

Findings

Derived four no-ghost and two sub-luminal constraints for stability.

Most models in the literature are found to be unstable or observationally unviable.

Generalized results to two-field configurations, highlighting potential ghost issues.

Abstract

We investigate the stability against inhomogeneous perturbations and the appearance of ghost modes in Gauss-Bonnet gravitational theories with a non-minimally coupled scalar field, which can be regarded as either the dilaton or a compactification modulus in the context of string theory. Through cosmological linear perturbations we extract four no-ghost and two sub-luminal constraint equations, written in terms of background quantities, which must be satisfied for consistency. We also argue that, for a general action with quadratic Riemann invariants, homogeneous and inhomogeneous perturbations are, in general, inequivalent, and that attractors in the phase space can have ghosts. These results are then generalized to a two-field configuration. Single-field models as candidates for dark energy are explored numerically and severe bounds on the parameter space of initial conditions are placed. A number of cases proposed in the literature are tested and most of them are found to be unstable or observationally unviable.