http://www.madsci.org/posts/1013049337.As.q.html

Your question was answered by:
Benjamin Monreal Grad student, Physics, MIT

Hello Dubi,

I think that your reasoning is mostly correct; the light we see today (in,
say, a Hubble Deep Field image) was actually emitted by the galaxies
billions of years ago; and, indeed, billions of years ago the galaxies
could have had different velocities than they do now. The Supernova
Cosmology Project, indeed, saw exactly this effect! They observed
supernovae up to seven billion light-years away, and showed that the
Universe was expanding faster at that time. That's exactly the importance
of these measurements: we can find a relationship between the Hubble
constant (how fast the Universe is expanding, i.e. the redshift) at various
times in its evolutions (i.e. the distance to the supernova, measured by
its brightness). The light-travel time is an important feature of this
measurement.

It's not just a simple model, though, asking "does it slow down or does it
speed up?" We have to predict how the Hubble constant would change under
various circumstances (gravity, a cosmological constant, dark matter, etc.)
and see whether these predictions agree or disagree with the data.

With the new supernova data, you cannot model the Universe as a bunch of
mass under the influence of only gravity. If gravity is the only force
acting on all of these galaxies and supernovae, then we cannot explain how
the Hubble constant (i.e. the expansion rate) has gotten from its old value
(measured by the distant supernovae) to its modern value (measured by the
nearby supernovae. Basically, in the past 7 billion years, things have not
slowed down as much as we expected them to. Observationally, we saw that
extremely redshifted supernova (SN1997ff was a good one) that were
unusually bright. Redshifted means fast expansion. Bright means nearby.
Combining the two, this supernovae is so nearby, that it can't have been
moving so fast for the whole lifetime of the Universe (taking into account
gravity, etc.) Therefore, the Universe must have started out with a slower
expansion, and accelerated. (Imagine that you
throw a baseball, wait one second, and open your eyes. If the baseball is
moving at 10 meters per second when you measure it, you would expect it to
be 10 meters away! If it is only 5 meters away, you can explain it by
saying that it started out slowly, and sped up to 10 m/s.)

Lots of good information on this topic can be found by going to
http://xxx.lanl.gov/find/astro-ph/ the Physics preprint archives
and searching for papers with "accelerating universe" in the title.
You'll find a mix of gritty-detail-technical papers, and a few easy-to-read
articles.

-Ben

Dubi, Lior and Oded.

I feel much more informed, though I am probably, not much wiser.

Processing will resume this Wednesday, when I have some free time.