Precision cosmology with Type Ia supernovae (SNe Ia) makes
use of the fact that SN Ia luminosities depend on their light-curve
shapes and colours. Using Supernova Legacy Survey (SNLS) and other data,
we show that there is an additional dependence on the global
characteristics of their host galaxies: events of the same light-curve
shape and colour are, on average, 0.08mag (~4.0sigma) brighter in
massive host galaxies (presumably metal-rich) and galaxies with low
specific star-formation rates (sSFR). SNe Ia in galaxies with a low sSFR
also have a smaller slope ("beta") between their luminosities and
colours with ~2.7sigma significance, and a smaller scatter on SN Ia
Hubble diagrams (at 95% confidence), though the significance of these
effects is dependent on the reddest SNe. SN Ia colours are similar
between low-mass and high-mass hosts, leading us to interpret their
luminosity differences as an intrinsic property of the SNe and not of
some external factor such as dust. If the host stellar mass is
interpreted as a metallicity indicator, the luminosity trends are in
qualitative agreement with theoretical predictions. We show that the
average stellar mass, and therefore the average metallicity, of our SN
Ia host galaxies decreases with redshift. The SN Ia luminosity
differences consequently introduce a systematic error in cosmological
analyses, comparable to the current statistical uncertainties on
parameters such as w. We show that the use of two SN Ia absolute
magnitudes, one for events in high-mass (metal-rich) galaxies, and one
for events in low-mass (metal-poor) galaxies, adequately corrects for
the differences. Cosmological fits incorporating these terms give a
significant reduction in chi^2 (3.8-4.5sigma). We conclude that future
SN Ia cosmological analyses should use a correction of this (or similar)
form to control demographic shifts in the galaxy population.
