  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.
