Hubble Tension and the G-step Model: Re-examination of Recent Constraints on Modified Local Physics

We critically examine recent claims challenging the viability of the G-step model (GSM) as a solution to the Hubble tension. The GSM proposes a $\sim$4 % increase in the effective gravitational constant $G_{\text{eff}}$ beyond $z \approx 0.01$ to reconcile local and early-universe measurements of the Hubble constant. Through detailed quantitative analysis, we demonstrate that many proposed constraints on the model require careful reconsideration. Key findings include: (1) Modern stellar modeling indicates a weaker $L \propto G^4$ scaling rather than the traditional $G^7$, significantly reducing tension with stellar evolution constraints; (2) The fluid-like behavior of Earth 150 Myr ago preserves the day/year ratio across any $G$ transition; (3) Paleoclimate data showing $\sim$20{\deg}C cooling over relevant timescales appears consistent with, rather than challenging, the GSM; (4) Distance indicator comparisons allow for $\Delta G/G$ variations up to $\sim$20 % at 2$\sigma$ when systematic uncertainties are properly included; (5) The discrete nature of the proposed $G$ transition preserves relative stellar population ages used in cosmic chronometry. When accounting for proper uncertainty levels in both observations and theoretical modeling, we find the GSM remains a viable candidate for resolving the Hubble tension. We identify specific observational tests with next-generation facilities that could definitively confirm or rule out the model.