Model-independent determination of cosmic curvature based on Pad\'{e} approximation

Abstract

Given observations of the standard candles and the cosmic chronometers, we apply Pad\'{e} parameterization to the comoving distance and the Hubble paramter to find how stringent the constraint is set to the curvature parameter by the data. A weak informative prior is introduced in the modeling process to keep the inference away from the singularities. Bayesian evidence for different order of Pad\'{e} parameterizations is evaluated during the inference to select the most suitable parameterization in light of the data. The data we used prefer a parameterization form of comoving distance as $D_{01}(z)=\frac{a_0 z}{1+b_1 z}$ as well as a competitive form $D_{02}(z)=\frac{a_0 z}{1+b_1 z + b_2 z^2}$. Similar constraints on the spatial curvature parameter are established by those models and given the Hubble constant as a byproduct: $\Omega_k = 0.25^{+0.14}_{-0.13}$ (68\% confidence level [C.L.]), $H_0 = 67.7 \pm 2.0$ km/s/Mpc (68\% C.L.) for $D_{01}$, and $\Omega_k = -0.01 \pm 0.13$ (68\% C.L.), $H_0 = 68.8 \pm 2.0$ km/s/Mpc (68\% C.L.) for $D_{02}$. The evidence of different models demonstrates the qualitative analysis of the Pad\'{e} parameterizations for the comoving distance.