I'm not sure if your question is about dark matter or dark energy. I'll answer first about dark energy, since it's fairly likely that dark matter is something like familiar matter, but consisting of particles which don't interact much with us except via gravity.
It's not clear how you go from the universe's lack of a center to the conclusion that other dimensions exist. Nonetheless, there are other chains of thought, mostly connected with integrating General Relativity and quantum mechanics, which suggest that there are likely to be some other dimensions.
There are now a number of efforts to do exactly what you propose: consider the effect of the contents of these other dimensions on the expansion of our space. Some concern tiny folded-up dimensions, and their contribution the energy density of space. Others, more recent, are more like what you're suggesting- parallel spaces separated by a small distance in another dimension, interacting with ours.
Getting back to dark matter, some of those ideas do suggest that dark matter also may be the effect of a nearby space. Fortunately these ideas are testable, and we should be hearing soon which fit better with detailed observations.
(published on 12/26/09)