You ask an interesting question and I know the straight forward answer which is: If the universe was rotating, it would be rotating about some axis and the Universe would have a preferred direction (along that axis). You're right that objects moving through the universe would appear to be repelled away from this axis by a "centrifugal force". But dark energy is driving objects away from us in all directions, not just perpendicular to some axis. So rotation can't explain dark energy. In other words, rotation tends to distribute things in a cylindrically symmetric manner, not in a fully spherically symmetric way.
I'm not sure if you know any quantum mechanics, but in case you do, I can also say that, though you might think that quantum mechanics could invalidate the classical argument given above, it turns out not to be true. The example I have in mind is the hydrogen atom where you could say that the electron in the ground state (or any S state) is spherically symmetric and it is "orbiting around the nucleus". However, these S states are exactly those states with no centrifugal force! (That is, they have no net angular momentum.) So, quantum mechanics lets you do something that you can't do classically: it lets you orbit a nucleus, but in just such a diffuse way that there is no centrifugal repulsion.
Again, it is the symmetry argument (cylindrical vs. spherical) that's important and quantum mechanics doesn't change that.
I hope this answers your question.
PS: If you haven't taken a class in quantum mechanics, but are interested in what I said above, you might look at equation (110) on the webpage: http://farside.ph.utexas.edu/teaching/qm/rotation/node7.html
The first term on the right is the attractive Coulomb term and the second
term is the repulsive centrifugal term. S states, however, are the states
with l=0, so the centrifugal term vanishes.
|last modified 12/16/2003 firstname.lastname@example.org|