Distance-Modulus Shift from Fifth-Coordinate Dark Energy: A Supernova Test of the Radius Drift

Type Ia supernovae measure distance moduli to a precision that now rivals the size of the effects a drifting fifth coordinate would produce. This paper integrates luminosity distances for the geometric dark-energy case with a constant equation of state and for the largest radius drift allowed by combined data, and converts the difference into distance-modulus shifts from redshift 0.1 to redshift 2. The maximal drift shifts moduli by a few hundredths of a magnitude at redshift one, comparable to the uncertainty of binned supernova samples and well above the shift produced by the frame's torsion components, which is effectively zero. Supernova cosmology therefore tests the geometric drift directly, and improved samples will either detect it or halve the allowed drift. Headline values are: shift at z1 max mag = -2.520e-02, shift at z0p5 max mag = -2.002e-02, shift at z2 max mag = -2.486e-02. This study is simulated and computed from stated assumptions; it is not a measurement.