  Type Ia supernova (SN Ia) cosmology provides the most direct evidence for the
presence of dark energy. This result is based on the assumption that the
look-back time evolution of SN Ia luminosity, after light-curve corrections,
would be negligible. Recent studies show, however, that the Hubble residual
(HR) of SN Ia is correlated with the mass and morphology of host galaxies,
implying the possible dependence of SN Ia luminosity on host galaxy properties.
In order to investigate this more directly, we have initiated spectroscopic
survey for the early-type host galaxies, for which population age and
metallicity can be more reliably determined from the absorption lines. As the
first paper of the series, here we present the results from high
signal-to-noise ratio (>100 per pixel) spectra for 27 nearby host galaxies in
the southern hemisphere. For the first time in host galaxy studies, we find a
significant (~3.9sigma) correlation between host galaxy mass (velocity
dispersion) and population age, which is consistent with the "downsizing" trend
among non-host early-type galaxies. This result is rather insensitive to the
choice of population synthesis models. Since we find no correlation with
metallicity, our result suggests that stellar population age is mainly
responsible for the relation between host mass and HR. If confirmed, this would
imply that the luminosity evolution plays a major role in the systematic
uncertainties of SN Ia cosmology.
