  Relatively uniform light curves and spectral evolution of Type Ia supernovae
(SNe Ia) have led to the use of SNe Ia as a ``standard candle'' to determine
cosmological parameters, such as the Hubble constant, the density parameter,
and the cosmological constant. Whether a statistically significant value of the
cosmological constant can be obtained depends on whether the peak luminosities
of SNe Ia are sufficiently free from the effects of cosmic and galactic
evolutions. Here we first review the single degenerate scenario for the
Chandrasekhar mass white dwarf (WD) models of SNe Ia. We identify the
progenitor's evolution and population with two channels: (1) the WD+RG
(red-giant) and (2) the WD+MS (near main-sequence He-rich star) channels. In
these channels, the strong wind from accreting white dwarfs plays a key role,
which yields important age and metallicity effects on the evolution. We then
address the questions whether the nature of SNe Ia depends systematically on
environmental properties such as metallicity and age of the progenitor system
and whether significant evolutionary effects exist. We suggest that the
variation of the carbon mass fraction $X$(C) in the C+O WD (or the variation of
the initial WD mass) causes the diversity of the brightness of SNe Ia. This
model can explain the observed dependence of SNe Ia brighness on the galaxy
types. Finally, applying the metallicity effect on the evolution of SN Ia
progenitors, we make a prediction of the cosmic supernova rate history as a
composite of the supernova rates in different types of galaxies.
