The Effects of the Gravitational Coupling Variation on the Local $H_0$ Estimation

We study the effects of the time evolution of the matter-gravity coupling on the luminosity distance, showing it can provide a natural explanation to the apparent Hubble tension. The gravitational coupling evolution induces a modification of the Friedman equation with respect to the $\Lambda$CDM model, which we study in both the Einstein and Jordan frame. We consider a phenomenological parametrization of the low redshift variation of the coupling in a narrow redshift shell, showing how it can affect the distance of the anchors used to calibrate supernovae (SNe), while higher redshift background observations are not affected. This effect is purely geometrical, and it is not related to any change of the intrinsic SNe physical properties. The effects of a time varying gravity coupling only manifest on sufficiently long time scales, such as in cosmological observations at different redshifts, and if ignored lead to apparent tensions in the values of cosmological parameters estimated with observations from different epochs of the Universe history.