Scalar mode propagation in modified gravity with a scalar field

TL;DR

This paper analyzes scalar mode propagation in modified gravity theories with a scalar field, revealing superluminal and light-speed modes, and discusses constraints and special cases in these models.

Contribution

It provides a general analysis of scalar perturbation propagation in modified gravity with a scalar field, highlighting the presence of superluminal modes and their characteristics.

Findings

Two scalar modes propagate with different speeds, including superluminal ones.

Scalar degrees of freedom do not alter the fundamental frequency dependence on wave vector.

Constraints on the models are discussed, with special cases analyzed.

Abstract

We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed.