Non-parametric modeling of the cosmological data, base on the $\chi^2$ distribution

TL;DR

This paper compares non-parametric methods like smoothing, genetic algorithms, and Gaussian processes for reconstructing the universe's expansion rate using recent cosmological data, employing chi-squared distribution for method selection.

Contribution

It introduces a chi-squared based criterion for selecting among non-parametric reconstruction methods in cosmology, applied to recent Hubble and supernova data.

Findings

Different methods yield consistent estimates of H_0.

Gaussian process provides the most reliable reconstruction.

Results contribute to understanding the Hubble tension.

Abstract

In the $\Lambda$CDM model, cosmological observations from the late and recent universe reveal a puzzling $\sim 4.5\sigma$ tension in the current rate of universe expansion. In addition to the various scenarios suggested to resolve the tension, non-parametric modeling may provide useful insights. In this paper, we look at three well-known non-parametric methods, the smoothing method, the genetic algorithm, and the Gaussian process. Considering these three methods, we employ the recent Hubble parameters data to reconstruct the rate of universe expansion and supernovae Pantheon sample to reconstruct the luminosity distance. In contrast to the similar studies in the literature, the chi-squared distribution has been used to construct a reliable criterion to select a reconstruction. Finally, we compute the current rate of universe expansion ($H_0$) for each method, provide some discussions regarding the performance of each approach, and compare the results.