Cosmological model-independent test of $\Lambda$CDM with two-point diagnostic by the observational Hubble parameter data

TL;DR

This study tests the $ ext{Lambda}$CDM cosmological model using observational Hubble data and a two-point diagnostic, finding results consistent with the model and supporting its viability without assuming specific cosmological parameters.

Contribution

It introduces a model-independent two-point diagnostic applied to binned Hubble data, providing a robust test of the $ ext{Lambda}$CDM model's validity.

Findings

The diagnostic remains consistent with $ ext{Lambda}$CDM within 1 $oldsymbol{\sigma}$ confidence.

Binning methods improve the signal-to-noise ratio of Hubble parameter measurements.

The $ ext{Lambda}$CDM model cannot be ruled out based on current observational data.

Abstract

Aiming at exploring the nature of dark energy (DE), we use forty-three observational Hubble parameter data (OHD) in the redshift range $0 < z \leqslant 2.36$ to make a cosmological model-independent test of the $\Lambda$CDM model with two-point $Omh^2(z_{2};z_{1})$ diagnostic. In $\Lambda$CDM model, with equation of state (EoS) $w=-1$, two-point diagnostic relation $Omh^2 \equiv \Omega_m h^2$ is tenable, where $\Omega_m$ is the present matter density parameter, and $h$ is the Hubble parameter divided by 100 $\rm km s^{-1} Mpc^{-1}$. We utilize two methods: the weighted mean and median statistics to bin the OHD to increase the signal-to-noise ratio of the measurements. The binning methods turn out to be promising and considered to be robust. By applying the two-point diagnostic to the binned data, we find that although the best-fit values of $Omh^2$ fluctuate as the continuous redshift intervals change, on average, they are continuous with being constant within 1 $\sigma$ confidence interval. Therefore, we conclude that the $\Lambda$CDM model cannot be ruled out.