Supernova Hubble Diagram Constraints on a Unified-Flow Model with Redshift-Dependent Fundamental Constants

Type Ia supernovae (SNe Ia) are luminous thermonuclear transients whose peak luminosities can be standardized, enabling measurements of luminosity distance over cosmological redshifts and an empirical Hubble diagram of distance modulus versus redshift that constrains the distance–redshift relation. Direct empirical tests in which redshift-dependent scalings of fundamental constants are applied to SN Ia distances remain scarce relative to fixed-constant interpretations. The aim is to determine whether a one-parameter unified-flow scaling of the distance scale can reproduce the Pantheon+SH0ES SN Ia Hubble diagram without introducing an explicit dark-energy term, and to quantify the resulting constraint on the scaling exponent. The model treats redshift evolution as a single coherent scaling that links the effective gravitational coupling and the light-propagation scale in a reciprocal manner, yielding an analytic luminosity-distance prediction under a matter-closure expansion law. The scaling exponent is estimated from Pantheon+SH0ES (1701 SNe Ia spanning redshifts 0.00122 to 2.26137) using the full statistical and systematic covariance matrix and an exact analytic profiling of the distance-modulus offset. The best fit is an exponent of negative 0.4975 (68% profile interval from negative 0.5165 to negative 0.4785) with a minimum chi-squared of 1751.82 for 1699 degrees of freedom; the fixed-constants matter-only baseline is disfavored by a chi-squared difference of 640.20, while a supernova-only flat Lambda CDM benchmark gives a matter density parameter of 0.3612 with an uncertainty of 0.0187 and a minimum chi-squared of 1752.51. After profiling the distance-modulus offset, the unified-flow and Lambda CDM distance laws differ by about 0.259 magnitudes at redshift 2.26137 and separate further at higher redshift. These results provide an empirically constrained, covariance-respecting phenomenological distance law consistent with current SN Ia distances and yield a falsifiable prediction for future higher-redshift standard candles or standard sirens.