Detectability of bigravity with graviton oscillations using
  gravitational wave observations
  The gravitational waveforms in the ghost-free bigravity theory exhibit
deviations from those in general relativity. The main difference is caused by
graviton oscillations in the bigravity theory. We investigate the prospects for
the detection of the corrections to gravitational waveforms from coalescing
compact binaries due to graviton oscillations and for constraining bigravity
parameters with the gravitational wave observations. We consider the bigravity
model discussed by the De Felice-Nakamura-Tanaka subset of the bigravity model,
and the phenomenological model in which the bigravity parameters are treated as
independent variables. In both models, the bigravity waveform shows strong
amplitude modulation, and there can be a characteristic frequency of the
largest peak of the amplitude, which depends on the bigravity parameters. We
show that there is a detectable region of the bigravity parameters for the
advanced ground-based laser interferometers, such as Advanced LIGO, Advanced
Virgo, and KAGRA. This region corresponds to the effective graviton mass of
$\mu \geq 10^{-17}~{\rm cm}^{-1}$ for $\tilde{c}-1 \geq 10^{-19}$ in the
phenomenological model, while $\mu \geq 10^{-16.5}~{\rm cm}^{-1}$ for
$\kappa\xi_c^2 \geq 10^{0.5}$ in the De Felice-Nakamura-Tanaka subset of the
bigravity model, respectively, where $\tilde{c}$ is the propagation speed of
the massive graviton and $\kappa\xi_c^2$ corresponds to the corrections to the
gravitational constant in general relativity. These regions are not excluded by
existing solar system tests. We also show that, in the case of $1.4-1.4M_{\rm
sun}$ binaries at the distance of $200~{\rm Mpc}$, $\log\mu^2$ is determined
with an accuracy of ${\cal O}$(0.1)\% at the 1$\sigma$ level for a fiducial
model with $\mu^2=10^{-33}~{\rm cm}^{-2}$ in the case of the phenomenological
model.
