Null test of the cosmic curvature using $H(z)$ and supernovae data

TL;DR

This paper presents a model-independent, geometrical null test of cosmic curvature using $H(z)$ and supernova data, employing Gaussian processes for reconstruction, and finds current data consistent with a flat universe.

Contribution

It introduces a novel, model-independent null test for cosmic curvature based on $H(z)$ and luminosity distance data using Gaussian processes.

Findings

Current data are consistent with a flat universe within 1 sigma.

Simulated future data can improve constraints on cosmic curvature.

The method is entirely geometrical and does not rely on specific cosmological models.

Abstract

We introduce a model-independent approach to the null test of the cosmic curvature which is geometrically related to the Hubble parameter $H(z)$ and luminosity distance $d_L(z)$. Combining the independent observations of $H(z)$ and $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature $\Omega_K^{(0)}$ in the null test relation. The null test is totally geometrical and without assuming any cosmological model. We show that the cosmic curvature $\Omega_K^{(0)}=0$ is consistent with current observational data sets, falling within the $1\sigma$ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different $\Omega_K^{(0)}$. Future observations in better quality can provide a greater improvement to constrain or refute the flat universe with $\Omega_K^{(0)}=0$.