2022ApJ...931..119Z

Although the spatial curvature has been precisely determined via observations of the cosmic microwave background by the Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which will allow us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter Ω_k in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with the future generation of the space-based Decihertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of ΔΩ_k = 0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon sample of Type Ia supernovae, which shows no evidence for a deviation from a flat universe at z ∼ 2.3. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution of Ω_k with redshift, through direct measurements of cosmic curvature at different redshifts (z ∼ 5). Such a model-independent Ω_k reconstruction to the distant past could become a milestone in gravitational-wave cosmology.