Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries

Abstract

If gravitation is propagated by a massive field, then the velocity of gravitational waves (gravitons) will depend upon their frequency as ${(v}_{g}{/c)}^{2}=1\ensuremath{-}(c/f{\ensuremath{\lambda}}_{g}{)}^{2}$, and the effective Newtonian potential will have a Yukawa form $\ensuremath{\propto}{r}^{\ensuremath{-}1}\mathrm{exp}(\ensuremath{-}r/{\ensuremath{\lambda}}_{g})$, where ${\ensuremath{\lambda}}_{g}{=h/m}_{g}c$ is the graviton Compton wavelength. In the case of inspiralling compact binaries, gravitational waves emitted at low frequency early in the inspiral will travel slightly slower than those emitted at high frequency later, resulting in an offset in the relative arrival times at a detector. This modifies the phase evolution of the observed inspiral gravitational waveform, similar to that caused by post-Newtonian corrections to quadrupole phasing. Matched filtering of the waveforms could bound such frequency-dependent variations in propagation speed, and thereby bound the graviton mass. The bound depends on the mass of the source and on noise characteristics of the detector, but is independent of the distance to the source, except for weak cosmological redshift effects. For observations of stellar-mass compact inspiral using ground-based interferometers of the LIGO-VIRGO type, the bound on ${\ensuremath{\lambda}}_{g}$ could be of the order of $6\ifmmode\times\else\texttimes\fi{}{10}^{12}$ km, about double that from solar-system tests of Yukawa modifications of Newtonian gravity. For observations of massive black hole binary inspiral at cosmological distances using the proposed Laser Interferometer Space Antenna (LISA), the bound could be as large as $6\ifmmode\times\else\texttimes\fi{}{10}^{16}$ km. This is three orders of magnitude weaker than model-dependent bounds from galactic cluster dynamics.