  (ABRIDGED) Recently, three important observational results were established:
(a) The evolution of the SNIa rate with redshift show that the rate rises up to
z~0.8, when the Universe was 6.5 Gyr old, and decreases afterward. (b) The rate
of supernova explosions of the different types as a function of the galaxy
(B-K) and the galaxy mass shows a marked increase with the star formation
activity. (c) The rate of SNIa in radio-loud galaxies is much higher than the
rate measured in radio-quiet galaxies. On this basis we have discussed the
distribution of the delay time (DTD) between the formation of a SNIa progenitor
star and its explosion as a SNIa. Our analysis finds: i) models with long delay
times, say 3-4 Gyr, cannot reproduce the dependence of the SNIa rate on the
colors and on the radio-luminosity of the parent galaxies; ii) the dependence
of the SNIa rate on the parent galaxy colors requires models with a wide DTD,
spanning the interval 100 Myr to 10 Gyr; iii) the dependence on the parent
galaxy radio-luminosity requires substantial production of SNIa at epochs
earlier than 100 Myr after the birth of a given stellar generation; iv) the
comparison between observed SN rates and a grid of theoretical
"single-population" DTDs shows that only a few of them are marginally
consistent with all observations; v) the present data are best matched by a
bimodal DTD, in which about 50% of type Ia SNe ("prompt" SNIa) explode soon
after their stellar birth, in a time of the order of 100 Myrs, while the
remaining 50% ("tardy" SNIa) have a much wider distribution, well described by
an exponential function with a decay time of about 3 Gyr. We discuss the
cosmological implications of this result and make simple predictions.
