AbstractIn order to estimate cosmic curvature from cosmological probes like standard candles, one has to measure the luminosity distance $$D_L(z)$$
D
L
(
z
)
, its derivative with respect to redshift $$D'_L(z)$$
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 $$\varDelta \varOmega _k= 0.09$$
Δ
Ω
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 $$\varDelta \varOmega _k= 0.13$$
Δ
Ω
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 $$\varOmega _k(z)$$
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.
KAGRA underground environment and lessons for the Einstein Telescope