The detection of gravitational waves ( GWs ) provides a direct way to measure the luminosity distance , which enables us to probe cosmology .
In this paper , we continue to expand the application of GW standard sirens in cosmology , and propose that the spatial curvature can be estimated in a model-independent way by comparing the distances from future GW sources and current cosmic-chronometer observations .
We expect an electromagnetic counterpart of the GW event to give the source redshift , and simulate hundreds of GW data from the coalescence of double neutron stars and black hole–neutron star binaries using the Einstein Telescope as reference .
Our simulations show that , from 100 simulated GW events and 31 current cosmic-chronometer measurements , the error of the curvature parameter \Omega _ { K } is expected to be constrained at the level of \sim 0.125 .
If 1000 GW events are observed , the uncertainty of \Omega _ { K } would be further reduced to \sim 0.040 .
We also find that adding 50 mock H ( z ) data ( consisting of 81 cosmic-chronometer data and 1000 simulated GW events ) could result in much tighter constraint on the zero cosmic curvature , for which , \Omega _ { K } = -0.002 \pm 0.028 .
Compared to some actual model-independent curvature tests involving the distances from other cosmic probes , this method with GW data achieves constraints with much higher precision .