  The present cosmic rate of Type Ia supernovae (SNeIa) suggests that about 6%
of all stars in binary systems with primaries in the initial mass range $3-9\
M\sun$ end up as SNeIa. If that is confirmed, the unavoidable conclusion is
that SNeIa can only be explained by the single degenerate scenario. At most 1%
of stars in binary systems in the above range end up as CO + CO WD pairs, with
total mass equal to or larger than the Chandrasekhar mass. Given that the
number of mergers from pairs of CO + He WDs that reach the Chandrasekhar mass
is even lower, the conclusion strongly favors binaries containing just one CO
WD as the progenitors of SNeIa, since the SNeIa production efficiency (relative
to the instantaneous star formation rate) predicted for double degenerate (DD)
pairs lies more than $3\sigma$ below the observational data, and the DD
scenario can be rejected at more than 99% confidence level. Only if the SFR
measurements from $z\sim 0.1$ to $z\sim 0.5$ are being underestimated by a
factor of 6 while SNeIa rates are not, can we escape the above conclusion. We
evaluate the numbers and characteristics of double WD systems with different
chemical compositions (CO and He WDs) that should form and compare them with
the observations, in order to check our predictions. Our conclusions appear
robust after that test.
