The AdS/CFT correspondance by now belongs to established knowledge and has many useful and interesting applications. Conversely, as far as I know it has not yet been possible to establish some kind of a ds/CFT correspondance in the same spirit. Are there any physics/mathematical reasons that such a dS/CFT like correspondance can never be found and proven?
More generally, what is the current state of the dS/CFT business today?
I got newly interested in this because in addition to the fact that a dS/CFT like relationship would be better suited to describe universes with a positive cosmological constant, a dS/CFT like correspondance could also help moving forward and generalize current efforts to prove the conjecture that any consistent quantum gravity has to be stringy. Such a proof is for example available for $AdS_3$ vacua
See also this interesting TRF article.