CORN -- Chronometers of Relic Nature I: The first estimate of the expansion rate of the Universe using compact relic galaxies
Measuring the expansion rate of the Universe is a central challenge in cosmology. Independent and robust methods are essential to validate existing measurements and assess potential systematic effects. We employ the cosmic chronometer (CC) approach, which uses the differential age evolution of quiescent galaxies to measure the Hubble parameter H(z) without assuming an underlying cosmological model. In contrast to previous CC studies, we restrict our analysis to relics -- ultra compact massive galaxies (UCMGs) hosting the oldest stellar populations -- thereby minimising uncertainties related to star formation history and merger history. We select a sample of 189 relic galaxies in the redshift range 0.07< z <0.22 from the E-INSPIRE UCMGs catalogue. Using the D_n4000 spectral index of relic galaxies and its redshift evolution, combined with MILES stellar population synthesis models, we derive the differential age relation required to infer H(z). We account not only for metallicity effects but also for the impact of alpha-element enhancement, which has not been explicitly propagated into the systematic uncertainty budget of the D_n4000 cosmic chronometer method. We obtain an independent measurement of H(z=0.15) = 85\pm53 km/s/Mpc. The total uncertainty is dominated by statistical limitations. The systematic component is 13% (8.7% when alpha-enrichment is not propagated), among the tightest estimates in current CC studies. We find that alpha-enrichment plays a major role in the systematic error budget, particularly in the high metallicity regime, and must be properly accounted for in future analyses. We demonstrate the proof of concept that relic galaxies provide a promising pathway to reduce systematic uncertainties in the CC method. The statistical uncertainties, which dominate the error budget, can be significantly reduced by the increase of data volume expected during the next years.