On Direct Estimation of Density Parameters and Hubble Constant for $Λ$CDM Universe using Hubble Measurements

Abstract: The set of cosmological density parameters ($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$, $\Omega_{0\Lambda}h_{0}^{2}$) and Hubble constant ($\hat{h}{0}$) are useful for fundamental understanding of the universe from many perspectives. In this article, we propose a new procedure to estimate these parameters for $\Lambda$ cold dark matter ($\Lambda$CDM) universe in the Friedmann-Robertson-Walker (FRW) background. We generalize the two-point statistics first proposed by Sahni et al. (2008) to the three point case and estimate the parameters using currently available Hubble parameter ($H(z)$) values in the redshift range $0.07 \leq z \leq 2.36$ measured by differential age (DA) and baryon acoustic oscillation (BAO) techniques. All the parameters are estimated assuming the general case of non-flat universe. Using both DA and BAO data we obtain $\Omega{0m}h_{0}^{2}=0.1485 \pm 0.0065$, $\Omega_{0k}h_{0}^{2}=-0.0137 \pm 0.017$, $\Omega_{0\Lambda}h_{0}^{2}=0.3126 \pm 0.0145$ and $\hat{h}_{0}=0.6689 \pm 0.0021$. These results are in satisfactory agreement with the Planck results. An important advantage of our method is that to estimate the value of any one of the independent cosmological parameters one does not need to use the values for the rest of them. Each parameter is obtained solely from the measured values of Hubble parameters at different redshifts without any need to use values of other parameters. Such a method is expected to be less susceptible to the undesired effects of degeneracy issues between cosmological parameters during their estimations. Moreover, there is no requirement of assuming spatial flatness in our method.