Cosmic CORALS: Timing the Universe with high-z star clusters

In this work, we explore the potential of anchoring the age-redshift relation across cosmic time by probing the oldest star clusters at high redshift, now observed thanks to the James Webb Space Telescope in strongly lensed fields. As a case study, we consider one of the highest-redshift systems observed, the Cosmic Gems arc at z=9.625. We perform image deconvolution of multi-band JWST imaging, identifying a total of 20 point sources along the arc. We derive the stellar ages through a cosmology-independent spectral energy distribution (SED) fitting framework, ensuring that these measurements can be used as unbiased cosmological anchors. By combining these high-z systems with state-of-the-art local globular cluster ages, we perform a joint Bayesian fit to the age-redshift relation in a flat CDM model, measuring H 0=70+27-16 and m=0.33+0.37-0.21. While these constraints are still loose, we show that the slope of the degeneracy, a power-law in the m - H 0 plane, is highly dependent on the redshift of the sources, becoming shallower as redshift increases. Leveraging this geometric rotation, we present forecasts showing that a future sample of about 300 lensed proto-globular clusters well-distributed up to z about 10 could tighten the statistical precision to 4% on H 0 and 11% on m, competitive with and independent of methods currently in use. The present work, therefore, represents a new avenue in cosmology and comes at a timely moment, when JWST observes high-redshift lensed star clusters routinely, Euclid and the Nancy Grace Roman Space Telescope uncover new strong lensing fields, and close to the start of operation of the ESO Extremely Large Telescope.