  DECIGO Pathfinder (DPF) has an ability to detect gravitational waves from
galactic intermediate-mass black hole binaries. If the signal is detected, it
would be possible to determine parameters of the binary components.
Furthermore, by using future space-borne gravitational wave interferometers, it
would be possible to test alternative theories of gravity in the strong field
regime. In this review article, we first explain how the detectors like DPF and
DECIGO/BBO work and discuss the expected event rates. Then, we review how the
observed gravitational waveforms from precessing compact binaries with slightly
eccentric orbits can be calculated both in general relativity and in
alternative theories of gravity. For the latter, we focus on Brans-Dicke and
massive gravity theories. After reviewing these theories, we show the results
of the parameter estimation with DPF using the Fisher analysis. We also discuss
a possible joint search of DPF and ground-based interferometers. Then, we show
the results of testing alternative theories of gravity using future space-borne
interferometers. DECIGO/BBO would be able to place 4--5 orders of magnitude
stronger constraint on Brans-Dicke theory than the solar system experiment.
This is still 1--2 orders of magnitude stronger than the future solar system
mission such as ASTROD I. On the other hand, LISA should be able to put 4
orders of magnitude more stringent constraint on the mass of the graviton than
the current solar system bound. DPF may be able to place comparable constraint
on the massive gravity theories as the solar system bound. We also discuss the
prospects of using eLISA and ASTROD-GW in testing alternative theories of
gravity. The bounds using eLISA are similar to the LISA ones, but ASTROD-GW
performs the best in constraining massive gravity theories among all the
gravitational wave detectors considered in this article.
