Model-independent measurement of cosmic curvature with the latest $H(z)$ and SNe Ia data: A comprehensive investigation

In the context of the discrepancies between the early and late universe, we emphasize the importance of independent measurements of the cosmic curvature in the late universe. We present an investigation of the model-independent measurement of the cosmic curvature parameter $\Omega_k$ in the late universe with the latest Hubble parameter $H(z)$ measurements and type Ia supernovae (SNe Ia) data. For that, we use two reconstruction methods, the Gaussian process (GP) and artificial neural network (ANN) methods, to achieve the distance construction from $H(z)$ data. Our analysis reveals that the GP method provides the most precise constraint on $\Omega_k$, with a constraint precision of $\xi(\Omega_k)=0.13$, surpassing recent estimations using similar methods. The GP method consistently indicates a preference for a flat universe at the 2$\sigma$ confidence level. Moreover, we find that the choice of reconstruction method influences the estimation of $\Omega_k$. The ANN reconstruction method exhibits higher sensitivity to the addition of BAO $H(z)$ data, resulting in comparable constraint precision to the GP method. A discrepancy exists between the best-fit values obtained by these two reconstruction methods, indicating their dependence on the reconstruction approach. However, we anticipate that with the improvement of sample size and precision of observational $H(z)$ data, the estimation of $\Omega_k$ using this approach will become more robust and reliable.Comment: 11 pages, 3 figures; accepted for publication in Physical Review