  Type Ia supernovae play a key role in the evolution of galaxies by polluting
the interstellar medium with a fraction of iron peak elements larger than that
released in the core collapse supernova events. Their light-curve, moreover, is
widely used in cosmological studies as it constitutes a reliable distance
indicator at extra-galactic scales. Among the mechanisms proposed to explain
the Type Ia SNe, the single and double degenerate channels are thought to be
the dominant ones, which imply a different distribution of time delays between
the progenitor formation and the explosion. In this paper, we aim at
determining the dominant mechanism by comparing a compilation of Type Ia SN
rates with those computed from various cosmic star formation histories coupled
with different delay time distribution functions, and evaluating the relative
contributions of both channels. By using a least-squares fitting procedure, we
model the observations of Type Ia SN rates assuming different combinations of
three recent cosmic star formation rates and seven delay time distributions.
The goodness of these fits are statistically quantified by the chi-squared
test. For two of the three cosmic star formation rates, the single degenerate
scenario provides the most accurate explanation for the observations, while a
combination of 34% single degenerate and 66% double degenerate delay time
distributions is more plausible for the remaining tested cosmic star formation
rates. The wide double degenerate scenario mechanism slightly under-predicts
the observations at redshift z>1, unless the cosmic SFR flattens in that
regime. On the contrary, although the purely close double degenerate scenario
can be ruled out, we cannot rule out a mixed scenario with single and double
degenerate progenitors.
