A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

TL;DR

This paper introduces a comprehensive method to parametrize linear cosmological perturbations in various gravity theories, specifically scalar-tensor and vector-tensor, enabling systematic analysis of their cosmological implications.

Contribution

It develops a general framework for parametrizing perturbations in gravity theories with any degrees of freedom, applied to scalar-tensor and vector-tensor theories, including higher-derivative corrections and specific subclasses.

Findings

Recovered known parametrizations for Horndeski and Beyond Horndeski theories.

Constructed the most general quadratic action for vector-tensor theories with second-order equations.

Identified free parameters needed to characterize these theories cosmologically.

Abstract

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.