Testing general relativity with binary black holes: a study on the sensitivity requirements for future space-based detectors

We study the sensitivity required for a future space-based detector to search for beyond general relativity effect in gravitational wave detection. To do this, we use the current design of TianQin, LISA, and $\mu$Ares as starting points, and study how their key noise parameters should be improved to adequately detect some target signals, for which we choose a nonlinear ringdown mode, displacement memory, and a putative beyond general relativity signal, all from the merger of massive black hole binaries. We find that the required improvements are strongly dependent on the choice of the target signals and the population model of massive black hole binaries, and $4-9$ orders of magnitude improvement will be needed in the most demanding detection scenarios.