Model-independent constraints on cosmic curvature. Implication from the future space gravitational-wave antenna DECIGO

In order to estimate cosmic curvature from cosmological probes like standard candles, one has to measure the luminosity distance D${}_L$(z), its derivative with respect to redshift D′${}_L$(z) and the expansion rate H(z) at the same redshift. In this paper, we study how such idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), in combination with cosmic chronometers providing cosmology-independent H(z) data. Our results show that for the Hubble diagram of simulated DECIGO data acting as a new type of standard siren, it would be able to constrain cosmic curvature with the precision of ΔΩ${}_k$ = 0.09 with the currently available sample of 31 measurements of Hubble parameters. In the framework of the third generation ground-based gravitational wave detectors, the spatial curvature is constrained to be ΔΩ${}_k$ = 0.13 for Einstein Telescope (ET). More interestingly, compared to other approaches aiming for model-independent estimations of spatial curvature, our analysis also achieve the reconstruction of the evolution of Ω${}_k$(z), in the framework of a model-independent method of Gaussian processes (GP) without assuming a specific form. Therefore, one can expect that the newly emerged gravitational wave astronomy can become useful in local measurements of cosmic curvature using distant sources.