Cosmic chronometers with galaxy clusters: a new avenue for multi-probe cosmology

We provide a new measurement of the expansion history of the Universe at $z=0.54$ with the cosmic chronometers (CC) method, exploiting the high-quality spectroscopic VLT/MUSE data for three galaxy clusters in close-by redshift bins: SDSS J2222+2745 ($z=0.49$), MACS J1149.5+2223 ($z=0.54$), and SDSS J1029+2623 ($z=0.59$). The central one, MACS J1149.5+2223, hosts the well-known supernova 'Refsdal', which allowed for $H_0$ measurements via time delay cosmography (TDC). This represents the first step for a self-consistent probe combination, where different methods are applied to the same data sample. After selecting the most passive and massive cluster members (38 CCs), we derive their age and physical parameters via full spectrum fitting. We use the code Bagpipes, specifically modified to remove the cosmological prior on ages. On average, the CC sample shows super-solar metallicities $Z/Z_{\odot} = 1.3 \pm 0.7$, low dust extinction $A_{\rm{V}} = 0.3 \pm 0.3$ mag and to have formed in short bursts $τ= 0.6 \pm 0.2$ Gyr. We also observe both an ageing trend in redshift and a mass-downsizing pattern. From the age-redshift trend, implementing the CC method through a bootstrap approach, we derive a new $H(z)$ measurement: $H$($z$=0.542) = $66_{-29}^{+81}$ (stat) $\pm$13 (syst) km/s/Mpc. We also simulate the impact of increased statistics and extended redshift coverage, finding that $H$($z$) uncertainties can be reduced by up to a factor of 4 with $\sim$100 CCs and a slightly broader redshift range (d$z\sim$0.2).