Snowflake,

The Perlmutter plot you link to *is* a distance versus time plot, shown exactly as you wish it to be, with distance on the y-axis, and time on the x-axis. Let's take a good, detailed look at the plot's axes.

The plot is of magnitude vs. redshift. More specifically, it is of magnitude vs. log(z). Magnitude goes as log(d)+constant, from the distance modulus. Redshift is (1/a)-1 {a is scale factor, the size of the universe}, and a goes like time to some power. (What the power is depends on, essentially, the temperature of the universe, and the precise value doesn't matter here.) So redshift goes as t^n-1, and log(z) goes as n*log(t)+constant. So the Perlmutter plot is basically of log(d) vs. log(t).

Since this is a log-log plot, a straight line is described by a slope of one, if it were exactly log(d) v. log(t). Since the plot is of a*log(d) vs. b*log(t), that slope is a/b. Any deviation from this slope, whether or not it is a straight line, is a curve on a d vs. t plot, and so corresponds to an acceleration. Further, since the slope seen is larger than a/b, there is an acceleration, not a deceleration, as distance increases more per unit time.

If you still think that the graph is time vs. velocity, please give me a detailed argument such as I have given you.

Dax