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Space-based gravitational-wave detectors, such as LISA or a similar ESA-ledmission, will offer unique opportunities to test general relativity. We studythe bounds that space-based detectors could place on the graviton Comptonwavelength \lambda_g=h/(m_g c) by observing multiple inspiralling black holebinaries. We show that while observations of individual inspirals will yieldmean bounds \lambda_g~3x10^15 km, the combined bound from observing ~50 eventsin a two-year mission is about ten times better: \lambda_g~3x10^16 km(m_g~4x10^-26 eV). The bound improves faster than the square root of the numberof observed events, because typically a few sources provide constraints as muchas three times better than the mean. This result is only mildly dependent ondetails of black hole formation and detector characteristics. The boundachievable in practice should be one order of magnitude better than this figure(and hence almost competitive with the static, model-dependent bounds fromgravitational effects on cosmological scales), because our calculations ignorethe merger/ringdown portion of the waveform. The observation that an ensembleof events can sensibly improve the bounds that individual binaries set on\lambda_g applies to any theory whose deviations from general relativity areparametrized by a set of global parameters.

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