Recalibrating Inflation: Insights from Starobinsky Gravity

Recent analyses of low-redshift supernova and Cepheid data reveal localized shifts in the distance modulus, often interpreted as calibration anomalies or hints of new physics. We propose that these features may emerge naturally from environment-dependent modifications to gravity. In particular, we examine the Starobinsky $f(R) = R + \lambda R^2$ model, which introduces a scalar degree of freedom that couples to ambient matter density and alters photon propagation in underdense regions. We derive the corresponding corrections to luminosity distance and show that they can reproduce the observed magnitude shifts without invoking discontinuities or empirical step functions. Statistical comparisons using AIC and BIC favor the Starobinsky framework over phenomenological models, supporting its role as a minimal, geometric explanation for emergent calibration transitions.