A gravitational constant transition within cepheids as supernovae calibrators can solve the Hubble tension

Local universe measurements of the Hubble constant (H0) using SNe Ia with Cepheids as calibrators yield a value of H0 which is in tension with the value inferred from the CMB and other higher redshift probes. In ref. [1], the authors proposed a rapid transition in the value of the effective Newtonian gravitational constant G in order to alleviate the Hubble tension. The transition point was chosen so as to only affect distance estimates to Hubble flow SNe. However, in this study, the authors made the assumption that SNe Ia peak luminosity $L$ increases with Chandrashekhar mass $M_c$. This hypothesis contradicts a previous semi-analytic study of SN light curves in the presence of G-transition [2] which found that $L\propto M_c^{-0.97}$. Motivated by the results of refs. [1] and [2], we propose a hypothesis of a sudden recent change in the effective G at an epoch which corresponds to a look-back distance between $\sim$ 7 - 80 Mpc. A transition in G at these distances would affect both our estimate of the distances to Cepheids in calibrator galaxies, as well as to the Hubble flow supernovae. Upon fitting the observational data to this hypothesis, we find three interesting results: (i) we find mild evidence for a G-transition at 22.4 Mpc (73 million years ago) which is preferred (using certain estimators) by the calibrator type Ia SNe data over no G-transition, (ii) the H0 parameter inferred under this hypothesis is in good agreement with the value obtained from the CMB for a 4% larger value of G at earlier times, thus potentially resolving the Hubble tension, (iii) we obtain a fit to the scaling relationship between SN peak luminosity $L$ and Chandrasekhar mass $M_c$, as $L\propto M_c^{-1.68 \pm 0.68}$, which is in good agreement with the prediction of the theoretical study of ref. [2]. We also discuss how other probes could be used to verify this transition in the value of G.