Time slowing down vs. universe expanding Einstein said that it is impossible to distinguish between the effect of gravity and acceleration (so if you stand in an accelerating elevator in space it would not feel any different than if you were in a gravitational field). My question is, can the same logic apply to the perceived expansion of the universe and time slowing down? In other words, can the redshift we see in galaxies be interpreted not as these galaxies accelerating away from us, but as these galaxies standing still but with time slowing down?
 A: Type Ia supernovas are good "standard candles" because their brightness follows a particular shape over several dozen days. Here's a pretty standard plot, cribbed from these lecture notes:

Notice that these are absolute brightnesses, already corrected for distance (which in this sample is known by other means, such as observations of Cepheid-type variable stars or other galaxies in nearby clusters) and for second-order effects like dust extinction.
You can see that the supernovae go from maximum brightness to obscurity in 20–60 days.
The correlation between the decay time and the brightness is not related to the apparent brightness of the supernova, as you would expect from a distance effect, but to its total brightness.
These supernovae have been observed with redshifts as large as at least $z\sim2$ (from the same source, credited to 2011 Nobel Laureate Reiss):

A redshift of $z=2 = \frac{a_\text{now}}{a_\text{then}}-1$ implies that the local scale factor at the time of the supernova was one-third what it is today.  If you want to attribute this to time running differently, you'd expect your forty-day brightness curve to extend over either 13 days or 120 days, I can't decide which. Either way, it'd be a huge difference between "local" and "distant" supernovae and there would be some other explanation discussed in the literature.
You suggest to me that you are confused between evidence for an expanding universe (known since Hubble in the 1920s) and evidence for a universe in which the rate of expansion is accelerating (known since 1998. Something for you to look for in your reading.
