An Improved Method to Measure the Cosmic Curvature

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 $1\sigma$.