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We analyze the stellar ages obtained from a combination of Lick indices inBorghi et al. for 140 massive and passive galaxies selected in the LEGA-Csurvey at $0.6<z<0.9$. From their median age--redshift relation, we derive anew direct measurement of $H(z)$ without any cosmological model assumptionusing the cosmic chronometer approach. We thoroughly study the main systematicsinvolved in this analysis: the choice of the Lick indices combination, thebinning method, the assumed stellar population model, and the adopted starformation history; these effects are included in the total error budget. Weobtain $H(z=0.75)= 98.8\pm33.6~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. In parallel, wealso propose a simple framework based on a cosmological model to describe theage--redshift relations in the context of galaxy downsizing. This allows us toderive constraints on the Hubble constant $H_0$ and the typical galaxyformation time. This new $H(z)$ measurement, whose accuracy is currentlylimited by the scarcity of the sample analyzed, paves the road for the jointstudy of the stellar populations of individual passive galaxies and theexpansion history of the Universe in light of future spectroscopic surveys.

Toward a Better Understanding of Cosmic Chronometers: A new measurement of H(z) at z~0.7