Stellar Evolution and the Cosmologial Supernovae Rates

We present the results of the population synthesis of the population ofthe supernovae progenitors. Both single and double degenerate progenitorsof SN Ia are considered. We compute the cosmic rate histories for SN I,SN II and both classes of SN Ia, and present them in the form of redshiftand magnitude distributions. These results can be compared with observationaldata, allowing to estimate the star formation rate history and thecosmological parameters including ω_baryons which cannot beestimated from analysing the Hubble diagrams of supernovae.We find that single degenerate (SD) SN Ia are younger than double degenerate (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 indifferent types of galaxies, or of different supernovae types forinterpretation of observations. These relative rates should be lessinfluenced by the selection effects than the absolute ones. This revised version was published online in July 2006 with corrections to the Cover Date.