An Improved Method to Measure the 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 $H_0=73.24\pm 1.74$ km ${\mathrm{s}}^{-1}$ $\mathrm{Mp}{\mathrm{c}}^{-1}$ gives a value of ${\Omega }_k$ a little bit above $1\sigma$ confidence level away from 0, but $H_0=69.6\pm 0.7$ km ${\mathrm{s}}^{-1}$ $\mathrm{Mp}{\mathrm{c}}^{-1}$ gives it below $1\sigma$.

9 pages, 5 figures, 2 tables. Accepted for publication in ApJ

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