Cosmological stability in f(ϕ,G) gravity - Shinji Tsujikawa (Physics Letters B, 2023)
In gravitational theories where a canonical scalar field ϕ with a potential V(ϕ) is coupled to a Gauss-Bonnet (GB) term G with the Lagrangian f(ϕ,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 G in f always induces Laplacian instability of a dynamical scalar perturbation associated with the GB term. This is also the case for f(G) gravity, where the presence of nonlinear GB functions f(G) is not allowed during the radiation- and matter-dominated epochs. A linearly coupled GB term with ϕ of the form ξ(ϕ)G can be consistent with all the stability conditions, provided that the scalar-GB coupling is subdominant to the background cosmological dynamics.