Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity

Abstract

In gravitational theories where a canonical scalar field $\varphi$ with a potential $V(\varphi )$ is coupled to a Gauss-Bonnet (GB) term $\mathcal{G}$ with the Lagrangian $f(\varphi ,\mathcal{G})$, we study the cosmological stability of tensor and scalar perturbations in the presence of a perfect fluid. We show that, in decelerating cosmological epochs with a positive tensor propagation speed squared, the existence of nonlinear functions of $\mathcal{G}$ in $f$ always induces Laplacian instability of a dynamical scalar perturbation associated with the GB term. This is also the case for $f(\mathcal{G})$ gravity, where the presence of nonlinear GB functions $f(\mathcal{G})$ is not allowed during the radiation- and matter-dominated epochs. A linearly coupled GB term with $\varphi$ of the form $\xi (\varphi )\mathcal{G}$ can be consistent with all the stability conditions, provided that the scalar-GB coupling is subdominant to the background cosmological dynamics.

13 pages, no figures

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