We study the performance of the latest $H(z)$ data in constraining the cosmological parameters of different cosmological models, including that of Chevalier-Polarski-Linder $w_0{w}_1$ parametrization. First, we introduce a statistical procedure in which the chi-square estimator is not affected by the value of the Hubble constant. As a result, we find that the $H(z)$ data do not rule out the possibility of either nonflat models or dynamical dark energy cosmological models. However, we verify that the time varying equation-of-state parameter $w(z)$ is not constrained by the current expansion data. Combining the $H(z)$ and the Type Ia supernova data, we find that the $H(z)/\mathrm{SNIa}$ overall statistical analysis provides a substantial improvement of the cosmological constraints with respect to those of the $H(z)$ analysis. Moreover, the $w_0-w_1$ parameter space provided by the $H(z)/\mathrm{SNIa}$ joint analysis is in very good agreement with that of Planck 2015, which confirms that the present analysis with the $H(z)$ and supernova type Ia (SNIa) probes correctly reveals the expansion of the Universe as found by the team of Planck. Finally, we generate sets of Monte Carlo realizations in order to quantify the ability of the $H(z)$ data to provide strong constraints on the dark energy model parameters. The Monte Carlo approach shows significant improvement of the constraints, when increasing the sample to 100 $H(z)$ measurements. Such a goal can be achieved in the future, especially in the light of the next generation of surveys.

• Received 11 September 2017

DOI:https://doi.org/10.1103/PhysRevD.97.063503