Search

We derive the equations of linear cosmological perturbations for the general Lagrangian density f (R,ϕ, X)/2 + Lc, where R is a Ricci scalar, ϕ is a scalar field, and X = -∂µ ϕ∂µ ϕ/2 is a field kinetic energy. We take into account a nonlinear self-interaction term Lc = ξ(ϕ) □ϕ(∂µ ϕ∂µ ϕ), which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds.