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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 $μ\geq 10^{-17}~{\rm cm}^{-1}$ for $\tilde{c}-1 \geq 10^{-19}$ in the phenomenological model, while $μ\geq 10^{-16.5}~{\rm cm}^{-1}$ for $κξ_c^2 \geq 10^{0.5}$ in the De Felice-Nakamura-Tanaka subset of the bigravity model, respectively, where $\tilde{c}$ is the propagation speed of the massive graviton and $κξ_c^2$ 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 $200~{\rm Mpc}$, $\logμ^2$ is determined with an accuracy of ${\cal O}$(0.1)\% at the 1$σ$ level for a fiducial model with $μ^2=10^{-33}~{\rm cm}^{-2}$ in the case of the phenomenological model.