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

TL;DR

This paper uses Padé approximation to model cosmic distances and determine the universe's curvature without relying on specific cosmological models, providing constraints consistent with current data.

Contribution

It introduces a model-independent method employing Padé parameterization for cosmic distances to constrain spatial curvature and compares different parameterization orders using Bayesian evidence.

Findings

Preferred Padé forms for comoving distance are identified.

Constraints on curvature parameter are consistent across models.

Bayesian evidence guides optimal model selection.

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.