Probing the Inhomogeneous Universe with Gravitational Wave Cosmology

If we assume that we live in the center of a spherical inhomogeneous universe, we can explain the apparent accelerating expansion of the universe without introducing the unknown dark energy or modifying gravitational theory. Direct measurement of the cosmic acceleration can be a powerful tool in distinguishing $\Lambda$CDM and the inhomogeneous models. If $\Lambda$CDM is the correct model, we have shown that DECIGO/BBO has sufficient ability to detect the positive redshift drift of the source by observing gravitational waves from neutron star binaries for 5-10 years. This enables us to rule out any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. Furthermore, by detecting the positive redshift drift at $z\sim 0$, we can even rule out generic LTB models unless we allow unrealistically steep density gradient at $z\sim 0$. We also show that the measurement accuracy is slightly improved when we consider the joint search of DECIGO/BBO and the third generation Einstein Telescope. This test can be performed with GW observations alone without any reference to electromagnetic observations.