Testing General Relativity through Gravitational Redshift with the Largest Spectroscopic Galaxy Cluster Catalogue

TThe ΛCDM model successfully describes the Universe but relies on unknown components like dark matter and dark energy (Λ). Deviations from General Relativity (GR) on large scales might explain these phenomena. Galaxy clusters, the largest gravitationally bound structures, offer ideal laboratories to test this possibility. A direct probe of the cluster’s gravitational potential is the gravitational redshift of its member galaxies. This subtle effect (∼ 10 km s−1) is easily overwhelmed by the galaxies’ peculiar velocity dispersion (∼ 1000 km s−1). Recovering this signal therefore requires stacking a large number of clusters and strictly accounting for observational biases and higher-order relativistic effects. Building upon Rosselli et al. (2023), we significantly increase the statistical power and validate our entire analysis pipeline using mock catalogues. We cross-match the recent WH24 cluster catalogue (Wen and Han 2024) with the SDSS DR16 spectroscopic galaxy sample (Ahumada et al. 2020), constructing the largest spectroscopic galaxy cluster catalogue assembled to date for gravitational redshift studies. We validate the stacking procedure and theoretical modelling, and we thoroughly investigate the critical impact of background subtraction and cluster recentering on the measurement. Finally, fitting the measured gravitational redshift profile with our validated theoretical model yields a scaling parameter of α = 0.99 ± 0.29, which is fully consistent with the predictions of GR.