A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

TL;DR

This paper unifies the analysis of linear cosmological perturbations across various modified gravity theories, establishing stability conditions, quasistatic approximations, and practical equations for computational modeling.

Contribution

It introduces a unified framework for scalar-tensor, vector-tensor, and bimetric theories, detailing stability criteria and quasistatic limits for cosmological perturbations.

Findings

All theories can be approximated by an effective Newton's constant and gravitational slip.

Identifies signatures to distinguish different classes of modified gravity models.

Provides equations suitable for implementation in Einstein-Boltzmann solvers.

Abstract

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.