Testing the Constancy of Type Ia Supernova Luminosities with Gaussian Process

Type Ia supernovae (SNe~Ia) are central to studies of cosmic expansion, under the assumption that their absolute magnitude $M_B$ does not evolve with redshift. Even small drifts in brightness can bias cosmological parameters such as $H_0$ and $w$. Here we test this assumption using a non-parametric Gaussian Process (GP) reconstruction of the expansion history from cosmic chronometer $H(z)$ data, which provides a model-independent baseline distance modulus, $\mu_{\rm GP}(z)$. To propagate uncertainties, we draw Monte Carlo realizations of $H(z)$ from the GP posterior and evaluate them on a Chebyshev grid, which improves numerical stability and quadrature accuracy. Supernova observations are then compared to this baseline through residuals, $\Delta M_B(z)$, and their derivatives. Applying this method to Pantheon+ (1701 SNe~Ia) and DES 5YR (435 SNe~Ia), we find that SNe~Ia are consistent with being standard candles within $1\sigma$, though both datasets exhibit localized departures: near $z \sim 1$ in Pantheon+ and at $z \sim 0.3$--$0.5$ in DES. The presence of similar features in two independent surveys suggests they are not purely statistical. Our results point toward a possible non-monotonic luminosity evolution, likely reflecting different physical drivers at different epochs, and highlight the need for a deeper astrophysical understanding of SN~Ia populations.