The Hubble tension, a significant discrepancy between the Hubble constant ($H_0$) values derived from early-time [cosmic microwave background (CMB) and baryon acoustic oscillations] and late-time [Cepheid-calibrated Type Ia Supernovae (SNe Ia)] 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 $d\lesssim 50\mathrm{Mpc}$ ($z\lesssim 0.01$). Specifically, we incorporate a gravitational transition causing a change in the gravitational constant ($G$) at a specific distance, affecting the Cepheid period-luminosity relation 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 semianalytical model in a recent theoretical study [Type Ia supernovae, standardizable candles, and gravity, Phys. Rev. D 97, 083505 (2018).]. Fixing $\mathrm{\Delta }G/G\approx 0.04$, 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.

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• Cosmic microwave background
• Cosmological parameters
• Dark energy