  Gravitational waves encode invaluable information about the nature of the
relatively unexplored extreme gravity regime, where the gravitational
interaction is strong, non-linear 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 various configurations the space-based
detector LISA. 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. 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.
