  We study different one-parametric models of type Ia Supernova magnitude
evolution on cosmic time scales. Constraints on cosmological and Supernova
evolution parameters are obtained by combined fits on the actual data coming
from Supernovae, the cosmic microwave background, and baryonic acoustic
oscillations. We find that data prefer a magnitude evolution such that
high-redshift Supernova are brighter than would be expected in a standard
cosmos with a dark energy component. Data however are consistent with
non-evolving magnitudes at the one-sigma level, except special cases.
  We simulate a future data scenario where SN magnitude evolution is allowed
for, and neglect the possibility of such an evolution in the fit. We find the
fiducial models for which the wrong model assumption of non-evolving SN
magnitude is not detectable, and for which at the same time biases on the
fitted cosmological parameters are introduced. Of the cosmological parameters
the overall mass density has the strongest chances to be biased due to the
wrong model assumption. Whereas early-epoch models with a magnitude offset ~z^2
show up to be not too dangerous when neglected in the fitting procedure, late
epoch models with magnitude offset ~sqrt(z) have high chances to bias the fit
results.
