Models for SNeIa and Evolutionary Effects with Redshift
  Based on detailed models for the explosions, light curves and NLTE-spectra, evolutionary effects of Type Ia Supernovae (SNe Ia) with redshift have been studied to evaluate their size on cosmological time scales,how the effects can be recognized and how one may be able to correct for them. We show that delayed detonation models can account for the majority of observations of spectra and LCs. IR observations are a new and powerful tools to constrain explosion models, e.g. by a strong MgII line at propagation in the WD. A strong Mg II line at 1.05 mu shows that nuclear burning takes place at the outer, low density layers. This requires a transition from the deflagration to the detonation regime of the nuclear burning front, or a very fast deflagration. We put the models into context with the empirical brightness decline relation which is widely applied to use SNe Ia as yardsticks on cosmological distance scales. This relation can be well understood in the framework of M(Ch)-WDs as a consequence of the opacity effects in combination with the amount of 56Ni which determines the brightness. We show that evolution may produce an offset in the brightness decline relation but it is restricted to a few tenth of a magnitude. Effects reveal themself by changes in the U and UV fluxes, and in a change in the maximum brightness/decline relation by DM is about 0.1Dt where Dt is the do difference between local and distant SN-samples. According to new data by Alde- ring et al.(2000), Dt<1day and, likely, evolution will not eliminate Lambda. 
Peter Hoeflich (Dept. of Astronomy, U.of Texas, Austin, USA)