Inflationary gravitational waves in the effective field theory of modified gravity

TL;DR

This paper derives the tensor perturbation spectrum during inflation within the effective field theory of modified gravity, encompassing various theories including Horndeski and Hořava-Lifshitz, and discusses implications for future CMB B-mode observations.

Contribution

It provides a unified framework to compute inflationary tensor spectra across a broad class of modified gravity theories, including higher-order spatial derivatives.

Findings

Derived second-order action for tensor perturbations in modified gravity.

Obtained inflationary power spectrum including higher-order corrections.

Mapped spectra in modified theories to General Relativity via disformal transformation.

Abstract

In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter background. We also show that the leading-order spectrum in concrete modified gravitational theories can be mapped on to that in General Relativity under a disformal transformation. Our general formula will be useful to constrain inflationary models from the future precise measurement of the B-mode polarization in the cosmic microwave background.