Comparison between the estimated integrated gravitational redshift signal up to 4r₅₀₀ and the theoretical predictions from GR (solid blue line), f(R) (dotted red line), and sDGP (dash-dotted green line) as a function of the cluster mass. The shaded coloured areas show the model errors, while the black points show the estimated . The vertical error bars represent the range of the parameter containing 68% of the marginalised posterior probability, while the horizontal error bars show the dispersion of the cluster masses in a given bin.