  One possibility for explaining the apparent accelerating expansion of the
universe is that we live in the center of a spherically inhomogeneous universe.
Although current observations cannot fully distinguish $\Lambda$CDM and these
inhomogeneous models, direct measurement of the acceleration of the universe
can be a powerful tool in probing them. We have shown that, if $\Lambda$CDM is
the correct model, DECIGO/BBO would be able to detect the positive redshift
drift (which is the time evolution of the source redshift $z$) in 3--5 year
gravitational wave (GW) observations from neutron-star binaries, which enables
us to rule out any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically
increasing density profile. We may even be able to rule out any LTB model
unless we allow unrealistically steep density profile at $z\sim 0$. This test
can be performed with GW observations alone, without any reference to
electromagnetic observations, and is more powerful than the redshift drift
measurement using Lyman $\alpha$ forest.
