Effects of a local physics change on the SH0ES determination of $H_0$

The Hubble tension, a significant discrepancy between the Hubble constant ($H_0$) values derived from early-time (Cosmic Microwave Background and Baryon Acoustic Oscillations) and late-time (Cepheid-calibrated Type Ia Supernovae) measurements, remains a major challenge in cosmology. Traditional attempts to resolve this tension have struggled to maintain consistency with dynamical and geometrical probes at redshifts $0.01<z\lesssim 2.5$. We explore a novel model introducing new degrees of freedom in local physical laws affecting calibrators like Cepheids and Type Ia Supernovae within a distance of $d\lesssim 50$ Mpc ($z\lesssim 0.01$). Specifically, we incorporate a gravitational transition causing a change in the gravitational constant ($G$) at a specific distance, affecting the Cepheid Period-Luminosity Relation (PLR) and the absolute magnitude of SNe Ia. We verify the inverse scaling of SN luminosity $L$ with Chandrasekhar Mass $M_C$ in a changed $G$ scenario as predicted using a semi-analytical model in a recent theoretical study \cite{Wright2018}. Fixing $\mathrm{\Delta }G\mathrm{/}G\approx 0.04$, our model naturally resolves the Hubble tension, yielding a best-fit $H_0$ value consistent with the Planck measurement, even without using Planck data. This approach suggests a potential resolution to the Hubble tension by aligning $H_0$ with high-redshift CMB measurements.