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 ${\lambda }_g=h/(m_{g}c)$ by observing multiple inspiralling black hole binaries. Observations of individual inspirals will yield mean bounds ${\lambda }_g\sim 3\times {10}^{15}$ km, but the combined bound from observing $\sim 50$ events in a two-year mission is about ten times better: ${\lambda }_g\simeq 3\times {10}^{16}$ km ($m_g\simeq 4\times {10}^{-26}$ 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.

Figure 1

Non-sky-averaged noise power spectral density $S^{\mathrm{NSA}}(f)$ for New LISA C2 (black, solid line), New LISA C5 (blue, dash-dotted line) and Classic LISA (red, dashed line).

Figure 2

Distribution of bounds on the graviton Compton wavelength for individual observations. We consider 1000 realizations of the massive BH population and three different detector designs: New LISA C2 (black, thick line), New LISA C5 (blue, medium line) and Classic LISA (red, dashed line).

Figure 3

Distribution of combined bounds over 1000 realizations of the MBH population. Line styles are as in Fig. 2.