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We study the advantage of the co-existence of future ground and space basedgravitational wave detectors, in estimating the parameters of a binarycoalescence. Using the post-Newtonian waveform for the inspiral of non-spinningneutron star-black hole pairs in circular orbits, we study how the estimatesfor chirp mass, symmetric mass ratio, and time and phase at coalescence areimproved by combining the data from different space-ground detector pairs.Since the gravitational waves produced by binary coalescence also provide asuitable domain where we can study strong field gravity, we also study thedeviations from general relativity using the parameterized post-Einsteinianframework. As an example, focusing on the Einstein telescope and DECIGO pair,we demonstrate that there exists a sweet spot range of sensitivity in thepre-DECIGO phase where the best enhancement due to the synergy effect can beobtained for the estimates of the post-Newtonian waveform parameters as well asthe modification parameters to general relativity.

Synergy between ground and space based gravitational wave detectors for estimation of binary coalescence parameters