High precision measurement of cosmic curvature: from gravitational waves
  and cosmic chronometer
  Although the spatial curvature has been measured with very high precision, it
still suffers from the well known cosmic curvature tension. In this paper, we
propose an improved method to determine the cosmic curvature, by using the
simulated data of binary neutron star mergers observed by the second generation
space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO).
By applying the Hubble parameter observations of cosmic chronometers to the
DECIGO standard sirens, we explore different possibilities of making
measurements of the cosmic curvature referring to a distant past: one is to
reconstruct the Hubble parameters through the Gaussian process without the
influence of hypothetical models, and the other is deriving constraints on
$\Omega_K$ in the framework of non-flat $\Lambda$ cold dark matter model. It is
shown that in the improved method DECIGO could provide a reliable and stringent
constraint on the cosmic curvature ($\Omega_{K} = -0.007\pm0.016$), while we
could only expect the zero cosmic curvature to be established at the precision
of $\Delta \Omega_K=0.12$ in the second model-dependent method. Therefore, our
results indicate that in the framework of methodology proposed in this paper,
the increasing number of well-measured standard sirens in DECIGO could
significantly reduce the bias of estimations for cosmic curvature. Such
constraint is also comparable to the precision of Planck 2018 results with the
newest cosmic microwave background (CMB) observations ($\Delta \Omega_{K}
\approx 0.018$), based on the concordance $\Lambda$CDM model.
