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

Abstract

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 $E^2=p^2c^2+{\mathbb A}\; p^{\alpha} c^{\alpha}$, 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 $\alpha \leq 1$, whereas for $\alpha > 1$, the bounds are weaker. We also study the effect of the spins of the compact binary constituents on the bounds.