Exploring the Systematic Uncertainties of Type Ia Supernovae as Cosmological Probes

We explore the systematic uncertainties of using Type Ia supernovae (SNe Ia) as cosmological probes, using the Supernova Legacy Survey Three Year data (SNLS3). We focus on studying the possible evolution of the stretch-luminosity parameter $\alpha$ and the color-luminosity parameter $\beta$, by allowing $\alpha$ and $\beta$ to be function of redshift, $z$. We find no evidence for the redshift evolution of $\alpha$. We find that without flux-averaging SNe, $\beta$ is consistent with being a constant when only statistical uncertainties are included, but it increases significantly with $z$ when systematic uncertainties are also included. The evolution of $\beta$ becomes marginal when all the SNe are flux-averaged, and $\beta$ is consistent with being a constant when only SNe at $z\ge 0.04$ are flux-averaged. Our results are insensitive to the lightcurve fitter used to derive the SNLS3 sample, or the functional form of $\alpha(z)$ and $\beta(z)$ assumed. It is likely that the apparent evolution of $\beta$ with $z$ for SNe without flux-averaging is a consequence of unknown systematic effects; flux-averaging reduces the impact of these effects by averaging them within each redshift bin. Assuming constant $\alpha$ and $\beta$, we find that the flux-averaging of SNe has a significant impact on the distance-redshift relation.