Constraint on ghost-free bigravity from gravitational Cherenkov radiation

Understand

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.