Probing general relativity: new measures of gravitational redshifts in galaxy clusters

In this Thesis work we test the Einstein theory of General Relativity by measuring the gravitational redshift effect in galaxy clusters, within the ΛCDM cosmological framework. To perform the gravitational redshift measurements, we create two new cluster member galaxies by exploiting the galaxy coordinates and spectroscopic redshifts derived from the sixteenth data release of the Sloan Digital Sky Survey, and two cluster catalogs, namely the Wen-Han-Liu cluster catalog (WHL15) and the cluster catalog derived from the latest data release of the Dark Energy Survey Instrument (DESI). We accurately estimate the cluster centers computing as the average of angular positions and redshifts of the closest galaxies to the Brightest Cluster Galaxy (BCG). We demonstrate that this choice provides a better approximation of the center of the cluster gravitational potential well relative to just assuming the BCG as the center, as done in the past literature works. We compare our measurements with the theoretical predictions of three different gravity theories: General Relativity, f (R) and the Dvali–Gabadadze–Porrati models (DGP). We implement a new statistical procedure in order to fit the measured gravitational redshift signal and consequently discriminate among the gravity theories. We clearly detect the gravitational redshift effect in both the exploited cluster catalogs. We recover an integrated gravitational redshift signal ∆ˆ mean,int = −11.4 ± 3.3 km s −1 for the WHL15 clusters, and ∆ˆ mean,int = −14.1 ± 3.6 km s −1 for the DESI cluster catalog. We get α = 0.86 ± 0.25, which is the free parameter of the new statistical analysis, from the WHL15 catalog, and α = 1.04 ± 0.28 from the DESI catalog. Thus, the gravitational redshift measurements are in agreement with the GR predictions considering both the cluster member catalogs (by construction α=1 in GR). Finally, we investigate the uncertainties possibly affecting our analysis.