We provide a new measurement of the expansion history of the Universe at z=0. 54 based on the cosmic chronometer (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 enabled H₀ measurements via time delay cosmography. 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 derived their age and physical parameters via full spectrum fitting. We used the code, which was specifically modified to remove the cosmological prior on ages. On average, the CC sample shows super-solar metallicities (Z/Z_⊙ = 1. 3 ± 0. 7) and a low dust extinction (A_ Bagpipes V = 0. 3 ± 0. 3 mag) and seems to have formed in short bursts (τ = 0. 6 ± 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) ±13 (syst) km/s/Mpc. We also simulated 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 ∼100 CCs and a slightly broader redshift range (dz∼0. 2).
Tomasetti et al. (Fri,) studied this question.