Gravitational waves and cosmic boundary

Space-based gravitational wave detectors have the capability to detect signals from very high redshifts. It is interesting to know if such capability can be used to study the global structure of the cosmic space. In this paper, we focus on one particular question: if there exists a reflective cosmic boundary at the high redshift ($z>15$), is it possible to find it? We find that, with the current level of technology: (1) gravitational waves appear to be the only means through which signatures from the cosmic boundary can possibly be detected; (2) a large variety of black holes, with masses roughly in the range $\mathcal{O}({10}^{3}--{10}^{6}){M}_{\ensuremath{\bigodot}}$, can be used for the task; (3) in the presumably rare but physically possible case that two merger events from the growth history of a massive black hole are detected coincidentally, a detector network like $\mathrm{TianQin}+\mathrm{LISA}$ is essential to help improve the chance to determine the orientation of the cosmic boundary; and (4) the possibility to prove or disprove the presence of the cosmic boundary largely depends on how likely one can detect multiple pairs of coincident gravitational wave events.