Stellar evolution and the cosmologial supernovae rates

We present the results of the population synthesis of the population of the supernovae progenitors. Both single and double degenerate progenitors of S N Ia are considered. We compute the cosmic rate histories for SN I, SN II a nd both classes of SN Ia, and present them in the form of redshift and magn itude distributions. These results can be compared with observational data, allowing to estimate the star formation rate history and the cosmological parameters including Omega(baryons) which cannot be estimated from analysin g the Hubble diagrams of supernovae. We find that single degenerate (SD) SN Ia are younger than double degenerat e (DD) ones, and so the SN Ia in elliptical galaxies should be mostly DD. We propose to use the redshift dependence of relative supernovae rates in d ifferent types of galaxies, or of different supernovae types for interpreta tion of observations. These relative rates should be less influenced by the selection effects than the absolute ones.