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

Abstract

Aiming at exploring the nature of dark energy (DE), we use forty-three observational Hubble parameter data (OHD) in the redshift range $0<z⩽2.36$ to make a cosmological model-independent test of the $\Lambda$CDM model with two-point $Om{h}^2(z_2;z_1)$ diagnostic. In $\Lambda$CDM model, with equation of state (EoS) $w=-1$, two-point diagnostic relation $Om{h}^2\equiv {\Omega }_m{h}^2$ is tenable, where ${\Omega }_m$ is the present matter density parameter, and $h$ is the Hubble parameter divided by 100 $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$. 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 $Om{h}^2$ 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.

Comments: 14 pages, 7 figures. Figures updated due to finding of a typo (thanks to Dr. Remudin Reshid Mekuria). arXiv admin note: text overlap with arXiv:1507.02517