Gravitational wave oscillations in bimetric cosmology

TL;DR

This paper investigates the behavior of gravitational wave oscillations in bimetric cosmology, revealing distinct regimes of tensor mode dynamics and improving analytical methods over previous approaches.

Contribution

It provides a detailed analysis of tensor mode dynamics in bimetric gravity near the GR limit, introducing new analytical techniques for different wavelength regimes.

Findings

Deep sub-horizon modes exhibit slowly evolving perturbations.

Large wavelength modes show fast oscillations.

The study improves upon previous WKB-based analyses.

Abstract

Unlike general relativity, in bimetric gravity linear gravitational waves do not evolve as free fields. In this theory there are two types of tensor perturbations, whose interactions are inherited from non-trivial couplings between two dynamical metric tensor fields in the Hassan-Rosen action, and are responsible for the phenomenon of bigravity oscillations. In this work, we analyze the dynamics of cosmological tensor modes in bimetric gravity on sub-horizon scales and close to the general relativity limit. In this limit, the system has a characteristic length scale $L$ that is strictly contained within the comoving Hubble radius. Thus, depending on the magnitude of the comoving wavelength $\lambda$ relative to $L$, we identify two regimes of interest where the system can be studied analytically: (i) deep sub-horizon modes with $\lambda\ll L$, whose dynamics can be studied using multiple scale analysis and are characterized by small and slowly evolving super-imposed perturbations; (ii) sub-horizon modes with $\lambda\gg L$, where the dynamics is characterized by fast super-imposed oscillations that can be studied using asymptotic techniques for highly oscillatory problems. Furthermore, our analysis represents a substantial improvement compared to previous analyses based on a generalization of the WKB method, which, as we show, is ill-suited to study the system at hand.