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Despite the tremendous success of general relativity so far, modifiedtheories of gravity have received increased attention lately, motivated fromboth theoretical and observational aspects. Gravitational wave observationsopened new possibilities for testing the viability of such theories in thestrong-field regime. One could test each theory against observed data one at atime, though a more efficient approach would be to first probe gravity in atheory-agnostic way and map such information to that on specific theoriesafterward. One example of such model-independent tests with gravitational wavesis the parameterized post-Einsteinian formalism, where one introduces genericparameters in the amplitude and phase that capture non-Einsteinian effects. Inthis paper, we derive gravitational waveforms from inspiraling compact binariesin various modified theories of gravity that violate at least one fundamentalpillar in general relativity. We achieve this by deriving relations betweencorrections to the waveform amplitude/phase and those to the frequencyevolution and Kepler's third law, since the latter two have already been (orcan easily be) derived in many theories. Such an analysis allows us to derivecorrections to the waveform amplitude, which extends many of previous worksthat focused on phase corrections only. Moreover, we derive gravitationalwaveforms in theories with varying gravitational constant. We extend theprevious work by introducing two gravitational constants (the conservative oneentering in the binding energy and the dissipative one entering in thegravitational wave luminosity) and allowing masses of binary constituents tovary with time. We also correct some errors in previous literature. Our resultscan be used to improve current analyses of testing general relativity as wellas to achieve new projected constraints on many modified theories of gravity.

Parameterized Post-Einsteinian Gravitational Waveforms in Various Modified Theories of Gravity