Parameterized and inspiral-merger-ringdown consistency tests of gravity with multi-band gravitational wave observations

The gravitational wave observations of colliding black holes have opened a new window into the unexplored extreme gravity sector of physics, where the gravitational fields are immensely strong, non-linear, and dynamical. 10 binary black hole merger events observed so far can be used to test Einstein's theory of general relativity, which has otherwise been proven to agree with observations from several sources in the weak- or static-field regimes. One interesting future possibility is to detect gravitational waves from GW150914-like stellar-mass black hole binaries with both ground-based and space-based detectors. We here demonstrate the power of testing extreme gravity with such multi-band gravitational-wave observations. In particular, we consider two theory-agnostic methods to test gravity using gravitational waves. The first test is the parameterized test where we introduce generic non-Einsteinian corrections to the waveform, which can easily be mapped to parameters in known example theories beyond general relativity. The second test is the inspiral-merger-ringdown consistency test where one derives the mass and spin of a merger remnant from the inspiral and merger-ringdown independently assuming general relativity is correct, and then check their consistency. In both cases, we use Fisher analyses and compare the results with Bayesian ones wherever possible. Regarding the first test, we find that multi-band observations can be crucial in probing certain modified theories of gravity, including those with gravitational parity violation. Regarding the second test, we show that future single-band detections can improve upon the current tests by roughly three orders of magnitude, and further 7-10 times improvement may be realized with multi-band observations.