I started looking around a little bit to figure out what is the empirical evidence that the expansion of the universe is accelerating.
If a plot of distance as a function of recession speed has a shallower slope at large recession speeds, then the universe was expanding more rapidly in the past than it is now. If a plot of distance versus recession speed is steeper at large recession speeds, then the universe was expanding more slowly in the past. (This verbal description, I realize, may be a bit confusing; a look at Figure 28-17 of the textbook should make things clearer.) : Universe (sixth edition) by Roger A. Freedman and William J. Kauffmann III (W. H. Freeman & Co., New York, 2002)
At minute #30:00 there is a graph showing that the expected feature of the standard cosmological model is in the opposite direction. Instead of getting a higher redshift as they look out at further supernova, they are getting a lower redshift.
If I am understanding everything right, the supernova data turned out opposite the way they should have expected if the Standard Model is correct. I think, though, if they really took a look at Milne's Model, they would find a much simpler explanation for the data that they have.