Projected constraints on the dispersion of gravitational waves using advanced ground- and space-based interferometers

Certain alternative theories of gravity predict that gravitational waves will disperse as they travel from the source to the observer. The recent binary black hole observations by Advanced-LIGO have set limits on a modified dispersion relation from the constraints on their effects on gravitational-wave propagation. Using an identical modified dispersion, of the form ${E}^{2}={p}^{2}{c}^{2}+\mathbb{A}{p}^{\ensuremath{\alpha}}{c}^{\ensuremath{\alpha}}$, where $\mathbb{A}$ denotes the magnitude of dispersion and $E$ and $p$ are the energy and momentum of the gravitational wave, we estimate the projected constraints on the modified dispersion from observations of compact binary mergers by third-generation ground-based detectors such as the Einstein Telescope and Cosmic Explorer as well as the space-based detector Laser Interferometer Space Antenna. We find that third-generation detectors would bound dispersion of gravitational waves much better than their second-generation counterparts. The Laser Interferometer Space Antenna, with its extremely good low-frequency sensitivity, would place stronger constraints than the ground-based detectors for $\ensuremath{\alpha}\ensuremath{\le}1$, whereas for $\ensuremath{\alpha}>1$, the bounds are weaker. We also study the effect of the spins of the compact binary constituents on the bounds.