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The $E_G$ statistic is a powerful probe for detecting deviations from GR bycombining weak lensing (WL), real-space clustering and redshift spacedistortion (RSD) measurements thus probing both the lensing and the growtheffective Newton constants ($G_L$ and $G_{eff}$). We construct an up to datecompilation of $E_G$ statistic data including both redshift and scaledependence ($E_G(R,z)$). We combine this $E_G$ data compilation with an up todate compilation of $f\sigma_8$ data from RSD observations to identify thecurrent level of tension between the Planck/$\Lambda$CDM standard model basedon general relativity and a general model independent redshift evolutionparametrization of $G_L$ and $G_{eff}$. Each $f\sigma_8$ datapoint consideredhas been published separately in the context of independent analyses ofdistinct galaxy samples. However, there are correlations among the datapointsconsidered due to overlap of the analyzed galaxy samples. Due to thesecorrelations the derived levels of tension of the best fit parameters withPlanck/$\Lambda$CDM are somewhat overestimated but this is the price to pay formaximizing the information encoded in the compilation considered. We find thatthe level of tension increases from about $3.5\sigma$ for the $f\sigma_8$ datacompilation alone to about $6\sigma$ when the $E_G$ data are also included inthe 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 effectiveNewton constant at low redshifts for both the lensing and the growth effectiveNewton constants ($G_L$ and $G_{eff}$)). These results further amplify thehints for weakening modified gravity discussed in other recent analyses.

Tension of the $E_G$ statistic and RSD data with Planck/$\Lambda$CDM and implications for weakening gravity