  Theoretical models predict that the initial metallicity of the progenitor of
a Type Ia supernova (SN Ia) affects the peak of the supernova light curve. This
can cause a deviation from the standard light curve calibration employed when
using SNe Ia as standardizable distance candles and, if there is a systematic
evolution of the metallicity of SN Ia progenitors, could affect the
determination of cosmological parameters. Here we show that this metallicity
effect can be substantially larger than has been estimated previously, when the
neutronisation in the immediate pre-explosion phase in the CO white dwarf is
taken into account, and quantitatively assess the importance of metallicity
evolution for determining cosmological parameters. We show that, in principle,
a moderate and plausible amount of metallicity evolution could mimic a
lambda-dominated, flat Universe in an open, lambda-free Universe. However, the
effect of metallicity evolution appears not large enough to explain the high-z
SN Ia data in a flat Universe, for which there is strong independent evidence,
without a cosmological constant. We also estimate the systematic uncertainties
introduced by metallicity evolution in a lambda-dominated, flat Universe. We
find that metallicity evolution may limit the precision with which Omega_m and
w can be measured and that it will be difficult to distinguish evolution of the
equation of state of dark energy from metallicity evolution, at least from SN
Ia data alone.
