Is gravity getting weaker at low z? Observational evidence and theoretical implications

Dynamical observational probes of the growth of density perturbations indicate that gravity may be getting weaker at low redshifts $z$. This evidence is at about $2-3\sigma$ level and comes mainly from weak lensing data that measure the parameter $S_8=\sigma_8 \sqrt{\Omega_{0m}/0.3}$ and redshift space distortion data that measure the growth rate times the amplitude of the linear power spectrum parameter $f\sigma_8 (z)$. The measured $f\sigma_8$ appears to be lower than the prediction of General Relativity (GR) in the context of the standard $\Lambda$CDM model as defined by the Planck best fit parameter values. This is the well known $f\sigma_8$ tension of $\Lambda$CDM, which constitutes one of the two main large scale challenges of the model along with the $H_0$ tension. We review the observational evidence that leads to the $f\sigma_8$ tension and discuss some theoretical implications. If this tension is not a systematic effect it may be an early hint of modified gravity with an evolving effective Newton's constant $G_{eff}$ and gravitational slip parameter $\eta$. We discuss such best fit parametrizations of $G_{eff}(z)$ and point out that they can not be reproduced by simple scalar-tensor and $f(R)$ modified gravity theories because these theories generically predict stronger gravity than General Relativity (GR) at low $z$ in the context of a $\Lambda$CDM background $H(z)$. Finally, we show weak evidence for an evolving reduced absolute magnitude of the SnIa of the Pantheon dataset at low redshifts ($z<0.1$) which may also be explained by a reduced strength of gravity and may help resolve the $H_0$ tension.