Density perturbations in general modified gravitational theories

TL;DR

This paper derives comprehensive linear perturbation equations for a broad class of modified gravity theories involving scalar fields and nonlinear self-interactions, facilitating the testing of dark energy models against observations.

Contribution

It provides a unified framework for analyzing linear cosmological perturbations in general scalar-tensor theories with nonlinear self-interactions, including Galileon models.

Findings

Derived equations for matter density perturbations and gravitational potentials.

Established conditions to avoid ghosts and Laplacian instabilities.

Included most dark energy models within the modified gravity paradigm.

Abstract

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, 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. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view.