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We compute the accuracy at which a LISA-like space-based gravitational wavedetector will be able to observe deviations from General Relativity in the lowfrequency approximation. To do so, we introduce six correction parameters thataccount for modified gravity in the second post-Newtonian gravitational wavephase for inspiralling supermassive black hole binaries with spin precession onquasi-circular orbits. Our implementation can be regarded as a subset of theppE formalism developed by Yunes and Pretorius, being able to investigate alsonext-to-leading order effects. In order to find error distributions for thealternative theory parameters, we use the Fisher information formalism andcarry out Monte Carlo simulations for 17 different binary black hole massconfigurations in the range 10^5 Msun < M < 10^8 Msun with 10^3 randomlydistributed points in the parameter space each, comparing the full (FWF) andrestricted (RWF) version of the gravitational waveform. We find that thebinaries can roughly be separated into two groups: one with low (< ~10^7 Msun)and one with high total masses (> ~10^7 Msun). The RWF errors on thealternative theory parameters are two orders of magnitude higher than the FWFerrors for high-mass binaries while almost comparable for low-mass binaries.Due to dilution of the available information, the accuracy of the binaryparameters is reduced by factors of a few, except for the luminosity distancewhich is affected more seriously in the high-mass regime. As an application andto compare our research with previous work, we compute an optimal lower boundon the graviton Compton wavelength which is increased by a factor of ~1.6 whenusing the FWF.

Testing General Relativity with LISA including Spin Precession and Higher Harmonics in the Waveform