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In this work, we achieve the determination of the cosmic curvature $Omega_K$ in a cosmological model-independent way, by using the Hubble parameter measurements $H(z)$ and type Ia supernovae (SNe Ia). In our analysis, two nonlinear interpolating tools are used to reconstruct the Hubble parameter, one is the Artificial Neural Network (ANN) method, and the other is the Gaussian process (GP) method. We find that $Omega_K$ based on the GP method can be greatly influenced by the prior of $H_0$, while the ANN method can overcome this. Therefore, the ANN method may have more advantages than GP in the measurement of the cosmic curvature. Based on the ANN method, we find a spatially open universe is preferred by the current $H(z)$ and SNe Ia data, and the difference between our result and the value inferred from Planck CMB is $1.6sigma$. In order to test the reliability of the ANN method, and the potentiality of the future gravitational waves (GW) standard sirens in the measurement of the cosmic curvature, we constrain $Omega_K$ using the simulated Hubble parameter and GW standard sirens in a model-independent way. We find that the ANN method is reliable and unbiased, and the error of $Omega_K$ is $sim0.186$ when 100 GW events with electromagnetic counterparts are detected, which is $sim56%$ smaller than that constrained from the Pantheon SNe Ia. Therefore, the data-driven method based on ANN has potential in the measurement of the cosmic curvature.
We use current measurements of the expansion rate $H(z)$ and cosmic background radiation bounds on the spatial curvature of the Universe to impose cosmological model-independent constraints on cosmic opacity. To perform our analyses, we compare opaci
Given observations of the standard candles and the cosmic chronometers, we apply Pad{e} parameterization to the comoving distance and the Hubble paramter to find how stringent the constraint is set to the curvature parameter by the data. A weak infor
Applying the distance sum rule in strong gravitational lensing (SGL) and type Ia supernova (SN Ia) observations, one can provide an interesting cosmological model-independent method to determine the cosmic curvature parameter $Omega_k$. In this paper
The question of whether Cosmic Microwave Background (CMB) temperature and polarization data from Planck favor a spatially closed Universe with curvature parameter $Omega_K<0$ has been the subject of recent intense discussions. Attempts to break the g
Inflation predicts that the Universe is spatially flat. The Planck 2018 measurements of the cosmic microwave background anisotropy favour a spatially closed universe at more than 2$sigma$ confidence level. We use model independent methods to study th