Towards a Better Understanding of Cosmic Chronometers: A new measurement of $H(z)$ at $z\sim0.7$

In this work, we analyze the stellar ages obtained from a combination of Lick indices in Borghi et al. (2021) [arXiv:2106.14894] for 140 massive and passive galaxies selected in the LEGA-C survey. The median estimated age-redshift relation is used to obtain a new direct measurement of $H(z)$ with the cosmic chronometers approach without any cosmological model assumption. We thoroughly study the main systematics involved in this analysis, including the choice of Lick indices combination, the binning method, the assumed stellar population model, and the adopted star formation history; these effects are included in the total error budget, obtaining $H(z=0.75)= 98.8\pm33.6$ km/s/Mpc. In parallel, we also propose a simple framework, based on a cosmological model, to describe the age-redshift relations in the context of galaxy downsizing. This allows us to derive constraints on the Hubble constant $H_0$ and the galaxy formation time. Our results add new fundamental elements to the cosmic chronometers approach by joining the detailed study of stellar populations of individual passive galaxies with the study of the expansion history of the Universe and show its potential in the light of upcoming spectroscopic surveys.