Can we discern any movement by the microwave background perpendicular to its expansion?
I hope one of the experts here will weigh in on this.
I am probably not understanding your question properly. But the cosmic radiation comes to us from all directions in space, so I am not sure how to even visualize what you mean by "perpendicular to its expansion." There is a certain sense in which the Earth (and the Milky Way galaxy) can be said to be moving, since the radiation is somewhat less redshifted in a certain direction than in the opposite direction, as measured by the COBE satellite a few years back.
Let me put it this way, Janitor (he who guards the door): is there any net rotataton of the universe from our perspective?
If we were to receive cooperation from alien civilizations living way out in a variety of places in the visible universe, each of them sending us radio transmissions (in English!) telling us what their own COBE-style detectors find in the way of anisotropies in the radiation, would we be able to piece the data together in a way that leads us to believe that the universe as a whole is rotating? Is that sort of what you are talking about? (As to what it would be rotating with respect to, I'll leave that to philosophers. )
Good enough. I. e., can cosmologically correlated redshifts (or anisotropies) in an expanding universe infer orbital motion as well?
You would probably need to break this down into a number of more tightly worded questions before it could, in principle, be amenable to testing.
Perhaps one way to approach this would be to ask what large scale variations there are in the SDSS data (you'll need just about the full SDSS dataset - not due for public release for several more years yet - because 2dF doesn't cover enough of the sky); you could look for both angular variations and distance/redshift ones.
Here's a paper, by Tegmark et al (including the SDSS consortium) which discusses some of the constraints on a range of cosmological parameters, from SDSS data and combined WMAP/SDSS data. The last sentence of the abstract: "Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened."
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