Theoretical physics implications of gravitational wave observation with future detectors

Gravitational waves encode invaluable information about the nature of the relatively unexplored extreme gravity regime, where the gravitational interaction is strong, nonlinear and highly dynamical. Recent gravitational wave observations by advanced LIGO have provided the first glimpses into this regime, allowing for the extraction of new inferences on different aspects of theoretical physics. For example, these detections provide constraints on the mass of the graviton, Lorentz violation in the gravitational sector, the existence of large extra dimensions, the temporal variability of Newton's gravitational constant, and modified dispersion relations of gravitational waves. Many of these constraints, however, are not yet competitive with constraints obtained, for example, through Solar System observations or binary pulsar observations. In this paper, we study the degree to which theoretical physics inferences drawn from gravitational wave observations will strengthen with detections from future detectors. We consider future ground-based detectors, such as the LIGO-class expansions A+, Voyager, Cosmic Explorer and the Einstein Telescope, as well as space-based detectors, such as various configurations of eLISA and the recently proposed LISA mission. We find that space-based detectors will place constraints on general relativity up to 12 orders of magnitude more stringently than current aLIGO bounds, but these space-based constraints are comparable to those obtained with the ground-based Cosmic Explorer or the Einstein Telescope (A+ and Voyager only lead to modest improvements in constraints). We also generically find that improvements in the instrument sensitivity band at low frequencies lead to large improvements in certain classes of constraints, while sensitivity improvements at high frequencies lead to more modest gains. These results strengthen the case for the development of future detectors, while providing additional information that could be useful in future design decisions.