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Abstract This review is focused on tests of Einstein’s theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein’s theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves are allowing us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamicalextreme gravity regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review then discusses gravitational-wave tests using compact binary systems, and ends with a description of the first gravitational wave observations by advanced LIGO, the stochastic gravitational wave background observations by pulsar timing arrays, and the tests that can be performed with them. 

Massive scalar fields are promising candidates for addressing many unresolved problems in fundamental physics. We report the first model-agnostic Bayesian search of massive scalar fields that are nonminimally coupled to gravity in LIGO/Virgo/KAGRA gravitational-wave data. We find no evidence for such fields and place the most stringent upper limits on their coupling for scalar masses $\lesssim 2\times {10}^{-12}\mathrm{eV}$. We exemplify the strength of these bounds by applying them to massive scalar-Gauss-Bonnet gravity, finding the tightest constraints on the coupling constant to date, $\sqrt{{\alpha }_{\mathrm{GB}}}\lesssim 1\mathrm{km}$for scalar masses $\lesssim {10}^{-13}\mathrm{eV}$to 90% credible level. Published by the American Physical Society2025