Modified gravity as a diagravitational medium

TL;DR

This paper explores how gravitational waves propagate in alternative gravity theories by modeling the extra gravitational degrees of freedom as a diagravitational medium with anisotropic dispersion, affecting wave behavior.

Contribution

It introduces the concept of a diagravitational medium with anisotropic properties to describe gravitational wave propagation in modified gravity theories.

Findings

Refractive index tensor accounts for wave deflection and modifications.

Most general media involve at least two independent tensors.

Provides a framework for understanding gravitational wave behavior in alternative theories.

Abstract

In this letter we reflect on the propagation of gravitational waves in alternative theories of gravity, which are typically formulated using extra gravitational degrees of freedom in comparison to General Relativity. We propose to understand that additional structure as forming a diagravitational medium for gravitational waves characterized by a refractive index. Furthermore, we shall argue that the most general diagravitational medium has associated an anisotropic dispersion relation. In some situations a refractive index tensor, which takes into account both the deflection of gravitational waves due to the curvature of a non-flat spacetime and the modifications of the general relativistic predictions, can be defined. The most general media, however, entail the consideration of at least two independent tensors.