Effective field theory approach to modified gravity including Horndeski theory and 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 Hořava-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 Hořava-Lifshitz gravity already derived in the literature.

27 pages

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Cited by in corpus (13)

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• A comparison of Einstein-Boltzmann solvers for testing General Relativity
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Anisotropic cosmological solutions in massive vector theories
• Observational signatures of the theories beyond Horndeski
• On the stability conditions for theories of modified gravity in presence of matter fields
• Inflationary gravitational waves in the effective field theory of modified gravity
• Cuscuta-Galileon cosmology: Dynamics, gravitational "constant"s and the Hubble Constant
• A General Model for Dark Energy Crossing the Phantom Divide
• Tackling non-linearities with the effective field theory of dark energy and modified gravity
• Separate Universes beyond General Relativity
• Absence of solid angle deficit singularities in beyond-generalized Proca theories
• Effective field theory of coupled dark energy and dark matter