The observational cosmology with distant Type Ia supernovae (SNe) as standard candles claims that the Universe is in accelerated expansion, caused by a large fraction of dark energy. In this paper we investigate the SN Ia environment, studying the impact of the nature of their host galaxies on the Hubble diagram fitting. The supernovae (192 SNe) used in the analysis were extracted from Joint-Light-curves-Analysis (JLA) compilation of high-redshift and nearby supernovae which is the best one to date. The analysis is based on the empirical fact that SN Ia luminosities depend on their light curve shapes and colors. We confirm that the stretch parameter of Type Ia supernovae is correlated with the host galaxy type. The supernovae with lower stretch are hosted mainly in elliptical and lenticular galaxies. No significant correlation between SN Ia colour and host morphology was found. We also examine how the luminosities of SNe Ia change depending on host galaxy morphology after stretch and colour corrections. Our results show that in old stellar populations and low dust environments, the supernovae are slightly fainter. SNe Ia in elliptical and lenticular galaxies have a higher $alpha$ (slope in luminosity-stretch) and $beta$ (slope in luminosity-colour) parameter than in spirals. However, the observed shift is at the 1-$sigma$ uncertainty level and, therefore, can not be considered as significant. We confirm that the supernova properties depend on their environment and that the incorporation of a host galaxy term into the Hubble diagram fit is expected to be crucial for future cosmological analyses.
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