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The direct detection of gravitational waves (GW) from merging binary blackholes and neutron stars mark the beginning of a new era in gravitationalphysics, and it brings forth new opportunities to test theories of gravity. Tothis end, it is crucial to search for anomalous deviations from generalrelativity in a model-independent way, irrespective of gravity theories, GWsources, and background spacetimes. In this paper, we propose a new universalframework for testing gravity with GW, based on the generalized propagation ofa GW in an effective field theory that describes modification of gravity atcosmological scales. Then we perform a parameter estimation study, showing howwell the future observation of GW can constrain the model parameters in thegeneralized models of GW propagation.

Generalized framework for testing gravity with gravitational-wave propagation. I. Formulation