7 Discussion

Although the bibliography of this review lists more than 500 references, fundamental tests of gravity remain the least explored sector of GW astronomy. It is also one where new discoveries may be hardest to come by – even if they would be momentous if they do. Space-based gravitational-wave detectors will improve certain existing constraints on alternative theories; even more important, they will provide novel and unique opportunities to precisely characterize the poorly explored nonlinear, dynamical sector of gravitation, as well as the properties of gravitational radiation fields. These measurements will provide a definite confirmation that Einstein’s theory, born from insight and beauty, applies in the most extreme regimes; or they may expose new phenomena, leading to new models for gravitational physics.

The research that we have reviewed spans a broad assortment of GW observations, which probe many disparate aspects of gravitational phenomenology. Some of these investigations have yet to be refined to the same level of formal rigor as other, more astrophysical applications of GW astronomy. Nevertheless, they paint an exciting picture of the expected fundamental-physics payoff of space-based detectors. We expect that this will remain an active and intriguing research area for many years: thus, it is appropriate that this review should be living, and we welcome the suggestions of our readers in improving it and keeping it up to date.