Constraint on ghost-free bigravity from gravitational Cherenkov radiation

TL;DR

This paper examines constraints on ghost-free bigravity models by analyzing gravitational Cherenkov radiation, finding that such radiation is suppressed for low graviton masses, aligning the model with cosmic ray observations.

Contribution

It derives conditions for gravitational Cherenkov radiation in ghost-free bigravity and estimates energy emission, providing constraints on model parameters based on cosmic ray data.

Findings

Cherenkov radiation is suppressed for graviton masses below 100 eV.

The model remains consistent with high-energy cosmic ray observations.

Conditions for Cherenkov radiation occurrence are explicitly derived.

Abstract

We investigate gravitational Cherenkov radiation in a healthy branch of background solutions in the ghost-free bigravity model. In this model, because of the modification of dispersion relations, each polarization mode can possess subluminal phase velocities, and the gravitational Cherenkov radiation could be potentially emitted from a relativistic particle. In the present paper, we derive conditions for the process of the gravitational Cherenkov radiation to occur and estimate the energy emission rate for each polarization mode. We found that the gravitational Cherenkov radiation emitted even from an ultrahigh energy cosmic ray is sufficiently suppressed for the graviton's effective mass less than $100\,{\rm eV}$, and the bigravity model with dark matter coupled to the hidden metric is therefore consistent with observations of high energy cosmic rays.