DECIGO/BBO as a Probe to Constrain Alternative Theories of Gravity

We calculate how strongly one can constrain the alternative theories of gravity with deci-Hz gravitational wave interferometers such as DECIGO and BBO. Here we discuss Brans-Dicke theory and massive graviton theories as typical examples. We consider the inspiral of compact binaries composed of a neutron star (NS) and an intermediate mass black hole (IMBH) for Brans-Dicke (BD) theory and those composed of a super massive black hole (SMBH) and a black hole (SMBH) for massive graviton theories. Using the restricted 2PN waveforms including spin effects and taking the spin precession into account, we perform the Monte Carlo simulations of 104 binaries to estimate the determination accuracy of binary parameters including the Brans-Dicke parameter ωBD and the graviton Compton length λg. Assuming a (1.4, 10)M⊙ NS/BH binary of SNR = √200, the constraint on ωBD is obtained as ωBD > 2.32 × 106, which is 300 times stronger than the estimated constraint from LISA observation. Furthermore, we find that, due to the expected large merger rate of NS/BH binaries of O(104) yr−1, a statistical analysis yields ωBD > 3.77 × 108, which is 4 orders of magnitude stronger than the current strongest bound obtained from the solar system experiment. For massive graviton theories, assuming a (106, 105)M⊙ BH/BH binary at 3 Gpc, one can put a constraint λg > 3.35 × 1020 cm, on average. This is three orders of magnitude stronger than the one obtained from the solar system experiment. From these results, it is also understood that DECIGO/BBO is a very powerful tool for constraining alternative theories of gravity.