re: Is there a special place in the Universe?
An author of the inscrutable paper, Sean says in the comments, "in this paper we are imagining a violation of translational invariance during inflation, which leaves an imprint on the CMB, but the laws of physics (and the vacuum state) are still translationally invariant. Imagine instead a “speck of dust†that was in our Hubble patch during inflation, and left its mark on the perturbations."
I don't get it. That isn't a preferred place, it's an example of an anisotropy magnified into an imprint in the CBR. I know it's my misunderstanding...