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

TL;DR

This paper investigates a model-independent method to measure cosmic curvature using the latest $H(z)$ and SNe Ia data, employing Gaussian process and neural network reconstructions, and finds a preference for a flat universe with improved precision.

Contribution

It introduces a comprehensive, model-independent approach using GP and ANN methods to constrain cosmic curvature from $H(z)$ and SNe Ia data, highlighting the impact of reconstruction techniques.

Findings

GP method yields the most precise $oxed{ ext{constraint}}$ on $oxed{ ext{cosmic curvature}}$ with $oxed{ ext{0.13}}$ precision.

GP analysis favors a flat universe at 2$ ext{σ}$ confidence level.

Reconstruction method choice significantly affects $oxed{ ext{curvature estimation}}$ and sensitivity to additional data.

Abstract

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.