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Link: http://www.arxiv.org/PS_cache/astro-ph/pdf/0605/0605611.pdf
Not published yet, but came across this interesting paper which did a sort of Michelson-Morley experiment but for the expansion of space.
The hypothesis being tested was that if local space was expanding, effects of this would show up if you let lasers lase in a pump and probe beam setup. They indicate that we now have the measurement capability to detect the effect, if it exists, and they did not find it.
Now mind you, this would measure local expansion of space, and in some variations of Big Bang Theory, local space (i.e. that around our galaxy) does not actually expand. The alternative being that local space would expand but gravity and electromagnetism would keep everything bound into smaller clusters.
(Of course, the other alternative being that there's no space expansion whatsoever... :) )
Another interesting link from ACG is a slideshow on MOND, that is, MOdified Newtonian Dynamics.
You may have heard of the search for Dark Matter. Part of this search is inspired by the problem with galactic rotation curves. Galaxies don't rotate as they should, based on the matter we can see.
There are a multitude of possibilities. Either it's normal matter that you just can't see (a lot of it), or it's "non-baryonic matter" (a la Star Trek when they get smucked by a cosmic string), or our equation of gravity doesn't work as well on galactic scales.
MOND takes the latter approach, and the drop-off in gravitational pull lessens as the distance from the center widens. Take a look-see at the slides.
The couple of alternative cosmology tidbits that could play on MOND. MOND dynamics are pretty similar to some of the 'pushing gravity' or 'LeSagian' systems I have previously read, where gravity is from a push force, not a pull force. MOND-type graphs can result from gravity particles that get absorbed.
Another relates to the MOND problem with galaxy mergers. I follow Arp on one particular thing in thinking that most galaxy mergers are actually ejections. If they are, it causes MOND fewer problems.