Calibrating Effective Ia Supernova Magnitudes using the Distance Duality
  Relation
  Using only Ia supernova (SN) observations, it is not possible to distinguish
the evolution of the SN absolute magnitude $M_B$ from an arbitrary evolution of
the Hubble parameter H(z). However, using Etherington's distance-duality
relation, which relates the angular and luminosity distances, together with the
observed angular baryon acoustic oscillation (BAO) scale at any redshift z, one
may calibrate an effective M(z). This calibration involves a scale which
depends on the cosmological model, however the evolution of the effective M(z)
between two redshifts with BAO observations is independent of this scale. The
line of sight BAO scale can be used to extend this calibration to redshifts
near z. As an application, using BOSS BAO at z=0.32 and 2.34, JLA supernova at
low $z$ and Hubble Space Telescope SN at z>1.7, we find a statistically
insignificant downward shift M(2.34)-M(0.32)=-0.08$\pm$0.15. Replacing BOSS
data with the best fit Planck LCDM BAO expectations, we find a shift of
-0.24$\pm$0.13. With the SN that will be observed by the James Webb Space
Telescope, such a calibration at z=2.34 will be more precise, and it will serve
as an anchor for cosmological analyses with the SN that it will observe at yet
higher z.
