Direct Measurement of the Positive Acceleration of the Universe and
  Testing Inhomogeneous Models under Gravitational Wave Cosmology
  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.
