Effective field theory approach to modified gravity including Horndeski theory and Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper reviews the effective field theory framework for modified gravity, encompassing Horndeski and Hořava-Lifshitz theories, deriving perturbation equations, and applying them to cosmological phenomena like inflation and dark energy.

Contribution

It provides a unified effective field theory approach that includes various modified gravity models and derives their perturbation dynamics on cosmological backgrounds.

Findings

Derived equations of motion for linear cosmological perturbations.

Applied framework to inflationary power spectra and dark energy models.

Confirmed stability conditions for Hořava-Lifshitz gravity.

Abstract

We review the effective field theory of modified gravity in which the Lagrangian involves three dimensional geometric quantities appearing in the 3+1 decomposition of space-time. On the flat isotropic cosmological background we expand a general action up to second order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories-- including Horndeski theory/its recent generalizations and the projectable/non-projectable versions of Ho\v{r}ava-Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Ho\v{r}ava-Lifshitz gravity already derived in the literature.