Determining the Hubble constant through the analysis of Abell clusters

The Hubble constant (H₀) quantifies the present-day expansion rate of the Universe and is a fundamental parameter for determining its age; however, modern cosmology faces significant tension, as increasingly precise measurements continue to yield mutually inconsistent values. The two main methods of measuring H₀, namely Cepheid variable stars and the Cosmic Microwave Background (CMB), have produced inconsistent results. Here, we present an alternative method to measure the expansion rate of the universe using galaxy clusters. We hypothesize that the relationship between cluster’s redshift and galaxy magnitude can yield a linear relation and produce a measurable value for H₀, assuming the fifth-brightest galaxy in each galaxy cluster has a consistent luminosity. Utilizing data from the Sloan Digital Sky Survey (SDSS) and the Abell Cluster Catalogue, redshifts were derived from SDSS optical spectra, and distances to the clusters were estimated under the assumption that member galaxies share similar brightness. The analysis yielded a H₀ value of 73.9 ± 11.4 km/s/Mpc, and the measurement, within uncertainty, remains consistent with the two leading methods of measuring H₀. This finding suggests that expanding the dataset to include more galaxy clusters is required to improve the accuracy of H₀ measurements.