Impact of the SNe Ia Magnitude Transition at 20 Mpc on Cosmological Parameter Estimation

We investigate the impact of a late-time transition in the standardized absolute magnitude $M$ on the best-fit values of cosmological parameters using the Pantheon+ dataset. Extending previous analyses which focused on flat $\Lambda$CDM, we examine this transition within flat $\Lambda$CDM, wCDM, and CPL cosmologies, as well as a model-independent cosmographic expansion, employing both frequentist ($\chi^2$ minimization with \textit{AIC}/\textit{BIC}) and Bayesian (MCMC and Nested Sampling) inference frameworks. We confirm that the data consistently favor a step in absolute magnitude of $\Delta M \simeq 0.19~\mathrm{mag}$ at a characteristic distance of $d_{\mathrm{crit}} \approx 20~\mathrm{Mpc}$. The inclusion of this transition leads to a statistically significant improvement in the quality of fit and has a distinct impact on parameter estimation: it induces a systematic increase in the inferred Hubble constant of approximately $2\%$ across all tested models. In contrast, we find that the dynamical parameters governing the background expansion, including the matter density $\Omega_m$ and the dark energy equation of state ($w_0, w_a$), remain stable and largely unaffected. These results indicate that the $20~\mathrm{Mpc}$ feature acts primarily as a low-redshift calibration shift rather than a modification of the late-time expansion history.