The Dark Energy Survey Supernova Program : slow supernovae show cosmological time dilation out to z ~ 1.

We present a precise measurement of cosmological time dilation using the light curves of 1504 type Ia supernovae from the Dark Energy Survey spanning a redshift range $0.1\\lesssim z\\lesssim 1.2$. We find that the width of supernova light curves is proportional to $(1+z)$, as expected for time dilation due to the expansion of the Universe. Assuming type Ia supernovae light curves are emitted with a consistent duration $\\Delta t_{\\rm em}$, and parameterising the observed duration as $\\Delta t_{\\rm obs}=\\Delta t_{\\rm em}(1+z)^b$, we fit for the form of time dilation using two methods. Firstly, we find that a power of $b \\approx 1$ minimises the flux scatter in stacked subsamples of light curves across different redshifts. Secondly, we fit each target supernova to a stacked light curve (stacking all supernovae with observed bandpasses matching that of the target light curve) and find $b=1.003\\pm0.005$ (stat) $\\pm\\,0.010$ (sys). Thanks to the large number of supernovae and large redshift-range of the sample, this analysis gives the most precise measurement of cosmological time dilation to date, ruling out any non-time-dilating cosmological models at very high significance....