Tension of the EG statistic and redshift space distortion data with the Planck-ΛCDM model and implications for weakening gravity

The E-G statistic is a powerful probe for detecting deviations from general relativity by combining weak lensing (WL), real-space clustering, and redshift space distortion (RSD) measurements, thus probing both the lensing and the growth effective Newton constants (G(L) and G(eff)). We construct an up-to-date compilation of E-G statistic data including both redshift and scale dependence [E-G(R, z)]. We combine this E-G data compilation with an up-to-date compilation of f sigma(8) data from RSD observations to identify the current level of tension between the Planck-Lambda CDM standard model based on general relativity and a general model-independent redshift evolution parametrization of G(L) and G(eff). Each f sigma(8) data point considered has been published separately in the context of independent analyses of distinct galaxy samples. However, there are correlations among the data points considered due to overlap of the analyzed galaxy samples. Due to these correlations, the derived levels of tension of the best-fit parameters with Planck-Lambda CDM are somewhat overestimated, but this is the price to pay for maximizing the information encoded in the compilation considered. We find that the level of tension increases from about 3.5 sigma for the f sigma(8) data compilation alone to about 6 sigma when the E-G data are also included in the analysis. The direction of the tension is the same as implied by the f sigma(8) RSD growth data alone [lower Omega(m) and/or weaker effective Newton constant at low redshifts for both the lensing and the growth effective Newton constants (G(L) and G(eff))]. These results further amplify the hints for weakening modified gravity discussed in other recent analyses.