An Improved Method to Measure the Cosmic Curvature

TL;DR

This study introduces an improved, model-independent approach combining recent Hubble parameter and supernova data to constrain cosmic curvature, confirming a flat universe with minimal dependence on supernova light-curve parameters.

Contribution

The paper presents a novel, model-independent method that jointly analyzes H(z) and SNe Ia data, revealing that cosmic curvature is consistent with zero and independent of supernova light-curve fitting parameters.

Findings

Cosmic curvature is consistent with zero within current observational uncertainties.

Different H(z) data samples do not significantly affect curvature constraints.

Hubble constant priors can influence the estimated value of cosmic curvature.

Abstract

In this paper, we propose an improved model-independent method to constrain the cosmic curvature by combining the most recent Hubble parameter $H(z)$ and supernovae Ia (SNe Ia) data. Based on the $H(z)$ data, we first use the model-independent smoothing technique, Gaussian processes, to construct distance modulus $\mu_{H}(z)$, which is susceptible to the cosmic curvature parameter $\Omega_{k}$. In contrary to previous studies, the light-curve fitting parameters, which account for distance estimation of SN ($\mu_{SN}(z)$), are set free to investigate whether $\Omega_{k}$ has a dependence on them. By comparing $\mu_{H}(z)$ to $\mu_{SN}(z)$, we put limits on $\Omega_{k}$. Our results confirm that $\Omega_{k}$ is independent of the SN light-curve parameters. Moreover, we show that the measured $\Omega_{k}$ is in good agreement with zero cosmic curvature, implying that there is no significant deviation from a flat Universe at the current observational data level. We also test the influence of different $H(z)$ samples and different Hubble constant $H_{0}$ values, finding that different $H(z)$ samples do not present significant impact on the constraints. However, different $H_{0}$ priors can affect the constraints of $\Omega_{k}$ in some degree. The prior of $H_{0}=73.24\pm1.74$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ gives a value of $\Omega_{k}$ a little bit above $1\sigma$ confidence level away from 0, but $H_{0}=69.6\pm0.7$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ gives it below $1\sigma$.