Is cosmic background radiation consistent with the Cosmological Principle? Is the observation of cosmic background radiation really consistent with the cosmological principle?  It implies that there is a "special" rest frame of motion with respect to the big bang.  I was of the impression the cosmological principle precluded any special frame on the largest scales of the universe as observations from every frame would be identical.
 A: It's ok. Compare the situation with having a house on planet Earth. To describe goings-on in the house, the rest frame of the house is a natural choice, a sort of "preferred frame". But this does not break the principle of relativity; it is not a "preferred frame" in that sense.
The frame in which, at the large scale, stuff in the universe is not moving, is a frame which stands out from all others as being a natural one to adopt to describe large-scale goings-on in the universe. This does not mean the principle of relativity is violated: Einstein's equation is still covariant.
Now let's come to the homogeneity, which is what cosmological principle asserts. This homogeneity means that the local universe is the same no matter where you happen to be, and the information arriving there from the rest of the universe is also the independent of location (on average). It does not mean that this information is independent of your state of motion relative to the standard frame (the cosmological co-moving frame). So for example, if you move relative to the standard frame then you will see the CMB red-shifted behind you and blue-shifted ahead of you. But this will be equally true if you are located anywhere else: that's what the homogeneity implies. So it is a homogeneity with respect to spatial location, not with respect to state of motion.
