The experimental determination of the cross-section of the ^{12}C+^{12}C
reaction has never been made at astrophysically relevant energies (E<2 MeV).
The profusion of resonances throughout the measured energy range has led to
speculation that there is an unknown resonance at E\sim1.5 MeV possibly as
strong as the one measured for the resonance at 2.14 MeV. We study the
implications that such a resonance would have for the physics of SNIa, paying
special attention to the phases that go from the crossing of the ignition curve
to the dynamical event. We use one-dimensional hydrostatic and hydrodynamic
codes to follow the evolution of accreting white dwarfs until they grow close
to the Chandrasekhar mass and explode as SNIa. In our simulations, we account
for a low-energy resonance by exploring the parameter space allowed by
experimental data. A change in the ^{12}C+^{12}C rate similar to the one
explored here would have profound consequences for the physical conditions in
the SNIa explosion, namely the central density, neutronization, thermal
profile, mass of the convective core, location of the runaway hot spot, or time
elapsed since crossing the ignition curve. For instance, with the largest
resonance strength we use, the time elapsed since crossing the ignition curve
to the supernova event is shorter by a factor ten than for models using the
standard rate of ^{12}C+^{12}C, and the runaway temperature is reduced from
\sim8.14\times10^{8} K to \sim4.26\times10^{8} K. On the other hand, a
resonance at 1.5 MeV, with a strength ten thousand times smaller than the one
measured at 2.14 MeV, but with an {\alpha}/p yield ratio substantially
different from 1 would have a sizeable impact on the degree of neutronization
of matter during carbon simmering. We conclude that a robust understanding of
the links between SNIa properties and their progenitors will not be attained
until the ^{12}C+^{12}C reaction rate is measured at energies \sim1.5 MeV.Comment: 15 pages, 6 tables, 10 figures, accepted for Astronomy and
Astrophysic