Signatures of explosion models of Type Ia supernovae and cosmology

Based on detailed models for the progenitors, explosions, light curves (LCs) and spectra, we discuss signatures of thermonuclear explosions, and the implications for cosmology. Consistency is needed to link observables and explosion physics. Type Ia supernovae (SNe Ia) most probably result from the explosion of a degenerate C/O-White Dwarf (WD) close to the Chandrasekhar mass. There is strong evidence that most of the WD is burned with an extended outer layer of explosive C-burning products (O, Ne, Mg) and very little C remaining. Overall, the chemical structure is radially stratified. This leads to the currently favored delayed detonation model in which a phase of slow nuclear burning as a deflagration front is followed by a detonation phase. The importance of pre-conditioning became obvious. Within an unified scenario, spherical models allow to understand both the homogeneity and basic properties of LCs and spectra, and they allow to probe for their diversity which is a key for high precision cosmology by SNe Ia. For local SNe Ia, the diversity becomes apparent by the combination of high-quality spectra and LCs whereas, for high-z objects, we will rely mostly on information from light curves. Therefore, we emphasize the relation between LC and spectral features. We show how we can actually probe the properties of the progenitor, its environment, and details of the explosion physics. We demonstrate the influence of the metallicity Z on the progenitors, explosion physics and the combined effect on light curves. By and large, a change of Z causes a shift of along the brightness-decline relation because Z shifts the balance between Ni-56 and non-radioactive isotopes but hardly changes the energetics or the Ni-56 distribution. However, the diversity of the progenitors produces an intrinsic dispersion in B-V which may pose a problem for reddening corrections. We discuss the nature of subluminous SN1999by, and how it can be understood in the same framework as 'normal-bright' SNe Ia. With the example of SN2003du, we show the influence of the progenitor system and distribution of isotopes on light curves. In both objects, we have seen clear evidence for some departure from sphericity, probably due to circumstellar interaction and stellar rotation, but the 3D signatures of deflagration fronts remain an elusive feature.