Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations

We study the bounds that space-based gravitational-wave detectors could realistically place on the graviton Compton wavelength λg=h/(mgc) by observing multiple inspiralling black hole binaries. Observations of individual inspirals will yield mean bounds λg~3×10¹⁵ km, but the combined bound from observing ~50 events in a two-year mission is about ten times better: λg3×10¹⁶ km (mg4×10^-26 eV). The bound improves faster than the square root of the number of observed events, because typically a few sources provide constraints as much as three times better than the mean. This result is only mildly dependent on details of black hole formation and detector characteristics. The bound achievable in practice should be an order of magnitude better than this figure, because our calculations ignore the merger/ringdown portion of the waveform.