| Abstract: Type Ia supernovae (SNe Ia) form the backbone of observational cosmology under the assumption that their absolute luminosities, once standardized, remain constant with redshift. Even small departures from this assumption can lead to systematic biases in key cosmological parameters, including the Hubble constant and the dark-energy equation of state. In this work, we test the redshift stability of SN Ia luminosities using a fully model-independent approach based on Gaussian Process (GP) reconstruction of the cosmic expansion history. We reconstruct the Hubble parameter $H(z)$ from cosmic chronometer measurements, which provide a direct, late-time probe of the expansion rate without reliance on an assumed cosmological model or early-Universe physics. The reconstructed expansion history is then used to obtain a baseline distance modulus, $\mu_{\rm GP}(z)$. To propagate uncertainties robustly and improve numerical stability, we generate Monte Carlo realizations of $H(z)$ from the GP posterior and evaluate the resulting integrals on a Chebyshev grid. Supernova data are compared against this baseline through luminosity residuals, $\Delta M_B(z)$, and their redshift dependence. Applying this framework to the Pantheon+ sample (1701 SNe Ia) and the DES 5-year sample (435 SNe Ia), we find that SNe Ia are broadly consistent with standard-candle behavior at the $1\sigma$ level. However, both datasets exhibit localized, non-monotonic deviations: near $z \sim 1$ in Pantheon+ and in the range $z \sim 0.3$–$0.5$ in DES. The presence of similar features in two independent surveys suggests that these deviations are unlikely to be purely statistical. Our results indicate the possibility of subtle, epoch-dependent luminosity variations in SN Ia populations and highlight the importance of disentangling astrophysical systematics from cosmological inference in the era of precision cosmology. |
