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 = - δμφδμφ/2 is a field kinetic energy. We take into account a nonlinear self-interaction term Lc = ξ(φ)φ(δμφδμφ), 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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)