We present a systematic study of the relationship between Type Ia Supernova ( SN Ia ) properties , and the characteristics of their host galaxies , using a sample of 581 SNe Ia from the full Sloan Digital Sky Survey II ( SDSS-II ) SN Survey .
We also investigate the effects of this on the cosmological constraints derived from SNe Ia .
Compared to previous studies , our sample is larger by a factor of > 4 , and covers a substantially larger redshift range ( up to z \sim 0.5 ) , which is directly applicable to the volume of cosmological interest .
We measure a significant correlation ( > 5 \sigma ) between the host-galaxy stellar-mass and the SN Ia Hubble Residuals ( HR ) .
We find a weak correlation ( 1.4 \sigma ) between the host-galaxy metallicity as measured from emission lines in the spectra , and the SN Ia HR .
We also find evidence that the slope of the correlation between host-galaxy mass and HR is -0.11 \mathrm { mag } / \mathrm { log } ( \mathrm { M } _ { \mathrm { host } } / \mathrm { M } _ { \odot } ) steeper in lower metallicity galaxies .
We test the effects on a cosmological analysis using both the derived best-fitting correlations between host parameters and HR , and by allowing an additional free parameter in the fit to account for host properties which we then marginalize over when determining cosmological parameters .
We see a shift towards more negative values of the equation of state parameter w , along with a shift to lower values of \Omega _ { \mathrm { m } } after applying mass or metallicity corrections .
The shift in cosmological parameters with host-galaxy stellar-mass correction is consistent with previous studies .
We find a best-fitting cosmology of \Omega _ { \mathrm { m } } = 0.266 _ { -0.016 } ^ { +0.016 } , \Omega _ { \Lambda } = 0.740 _ { -0.018 } ^ { +0.018 } and w = -1.151 _ { -0.121 } ^ { +0.123 } ( statistical errors only ) .