Constraint on ghost-free bigravity from gravitational Cherenkov
  radiation
  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.
