Graviton Mass from Close White Dwarf Binaries Detectable with LISA

The arrival times of gravitational waves and optical light from orbiting binaries provide a mechanism to understand the propagation speed of gravity when compared to that of light or electromagnetic radiation. This is achieved with a measurement of any offset between optically derived orbital phase related to that derived from gravitational wave data, at a specified location of one binary component with respect to the other. Using a sample of close white dwarf binaries (CWDBs) detectable with the Laser Interferometer Space Antenna (LISA) and optical light curve data related to binary eclipses from meter-class telescopes for the same sample, we determine the accuracy to which orbital phase differences can be extracted. We consider an application of these measurements involving a variation to the speed of gravity, when compared to the speed of light, due to a massive graviton. For a subsample of $\sim$ 400 CWDBs with high signal-to-noise gravitational wave and optical data with magnitudes brighter than 25, the combined upper limit on the graviton mass is at the level of $\sim 6 \times 10^{-24}$ eV. This limit is two orders of magnitude better than the present limit derived by Yukawa-correction arguments related to the Newtonian potential and applied to the Solar-system.