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. 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 describe the single degenerate scenario for the Chandrasekhar mass white dwarf (WD) models of SNe Ia. 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 dependences of SNe Ia brightness on the galaxy types and the distance from the galactic center. If X(C) primarily determines the brightness and light-curve shape of SNe Ia, the light, curve shape (LCS) method, which determines the absolute peak luminosity, should be valid at high-z.
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