Calibrating High Redshift Ia Supernovae 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). 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 M_B(z). This calibration involves a scale which depends on the cosmological model, however the evolution of M_B(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 that M_B(2.34)-M_B(0.32)=-0.11$\pm$ 0.16. This statistically insignificant downwards shift results from Malmquist bias and brighter than expected high z SN. Replacing BOSS data with the best fit Planck LCDM BAO expectations, we find a shift of -0.26$\pm$ 0.15. 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.