Cosmological Parameter Estimation using $H(z)$ Measurements for Nonflat $\Lambda$ Cold Dark Matter Universe
Abstract
Accurate estimations of cosmological density parameters ($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$, $\Omega_{0\Lambda}h_{0}^{2}$) and Hubble constant ($h_{0}$) provide detailed understanding of our universe. We propose a new procedure to estimate these parameters for nonflat $\Lambda$CDM universe in the FriedmannRobertsonWalker (FRW) background. We utilize the Hubble parameter ($H(z)$) measurements in our analysis. These $H(z)$ are measured using two techniques (DA and BAO). We generalize the twopoint diagnostic method first proposed by Sahni et al.(2008) to the case of nonflat spatial curvature of the universe. Using three independent $H(z)$ measurements at a time, we solve for three fundamental cosmological density parameters ($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$, $\Omega_{0\Lambda}h_{0}^{2}$) and repeat the procedure for all possible combinations of three measurements of Hubble parameters. We divide the $H(z)$ data into three groups comprising all, $31$ DA only and $24$ BAO only measurements. We perform our analysis separately on each group. In our method, we use weightedmean and median statistics to estimate the values of density parameters. Using these estimated values of density parameters, we also find the values of $h_{0}$ for each of these three sets corresponding to each of two statistics. We conclude that median statistic is more reliable in our analysis, since the sample specific uncertainties are nonGaussian in nature. Finally, we achieve the reliable results $\Omega_{0m}h_{0}^{2}=0.1485^{+0.0041}_{0.0051}$, $\Omega_{0k}h_{0}^{2}=0.0137^{+0.0129}_{0.0125}$, $\Omega_{0\Lambda}h_{0}^{2}=0.3126^{+0.0131}_{0.009}$ and $h_{0}=0.6689^{+0.0141}_{0.0121}$ using median statistic in our analysis corresponding to the set of total $53$ $H(z)$. Our estimated median values of cosmological parameters agree with Planck Collaboration VI.(2020) results excellently.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 arXiv:
 arXiv:2204.07099
 Bibcode:
 2022arXiv220407099P
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 14 pages, 6 figures