Gauge-ready formulation of cosmological perturbations in scalar-vector-tensor theories

TL;DR

This paper develops a comprehensive gauge-ready framework for analyzing cosmological perturbations in scalar-vector-tensor theories, enabling flexible gauge choices and revealing conditions for stability and observational implications in models of dark energy, inflation, and nonsingular cosmologies.

Contribution

It introduces a versatile, gauge-ready formulation for SVT theories that includes Horndeski and Proca theories, facilitating stability analysis and observational comparisons without fixing gauges.

Findings

Framework covers Horndeski and Proca as special cases.

Conditions for avoiding ghost and Laplacian instabilities are derived.

Separation of observables into tensor, vector, scalar sectors is clarified.

Abstract

In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history.