Cosmography with DESI-DR1 Cosmic Chronometers: Direct H(z) measurements from Luminous Red Galaxy ages

Providing robust redshift estimates for almost 3 million luminous red galaxies (LRGs), the Dark Energy Spectroscopic Instrument (DESI) offers a unique opportunity to test the expansion rate of the Universe with independent approaches. We apply the cosmic chronometer method to derive new, independent constraints on the Hubble parameter at 0.3<z<1.2 from the differential age evolution of DESI LRGs. We select spectra applying spectroscopic cuts to ensure sample purity and remove contamination by star-forming objects, then build a robust sample of cosmic chronometers (CCs) by stacking to obtain stable, high signal-to-noise (S/N) spectra, which also serves as a democratic binning choice for the $t-z$ plane. Ages are estimated by measuring Lick indices on the stacked spectra and fitting them with a theoretical stellar population model. We obtain $t-z$ relations from which we derive $H(z)$ constraints via two independent approaches: a fit with a pivotal-redshift cosmography, and a direct estimate from the original CC method. The cosmographic fit yields posteriors for the kinematic parameters $\{H_{z_0},q_{z_0},j_{z_0}\}$ compatible with currently considered cosmologies, giving a precision-level estimate of $H(z)$. We provide the maximum-a-posteriori (MAP) $H(z)$ estimate, an array of the median confidence region in the $H-z$ plane, and its covariance matrix. We also leverage the redshift distributions of the $t-z$ relation for different velocity dispersion groups to obtain two independent local measurements using the discrete approximation $H(z)\approx -\mathrm{\Delta }z\mathrm{/}[\mathrm{\Delta }t(1+z)]$; the one from the reddest envelope of CCs gives $H(z\approx 0.61)=88.5_{-12.6}^{+6.7}$ (stat.) $\pm 8.1$ (syst.) km s${}^{-1}$ Mpc${}^{-1}$. Systematic uncertainties for both the cosmographic and discrete $H(z)$ measurements come from a comprehensive analysis of all methodological choices in the data treatment.