Issues with de Sitter Space and Conformal Field Theory As a de Sitter universe is more convenient for cosmology, what are the current issues with a dS/CFT type correspondence? Earlier work by Strominger, seemed promising but I haven't heard of additional developments and I was wondering about the challenges facing such a theory.
Clarification: Since de Sitter spacetimes are dual to Euclidean conformal field theories, is a dS/CFT correspondence hopeless to reproduce the dynamics of quantum field theories and gravity?    
 A: The fact that a bulk theory is dual to a field theory on the boundary is really nothing special. Maxwell's equations are dual to the constraint field theory on boundary conditions. The problem is that the field theory is typically some weird composite, for instance a combination of an initial and boundary condition for Maxwell will give $div \vec{B}$ on the initial conditions and the projection of the rest into the boundary.
Similarly, the conformal infinity in AdS is a boundary requiring the specification of boundary conditions in the sense that there is no complete Cauchy surface in the AdS space-time on its own. For details see the following paper and references therein: Helmut Friedrich (1995), Einstein equations and conformal structure: Existence of Anti-de Sitter type space-times. But the point of AdS is also that the boundary is a really nice place, Minkowski, and there are no weird composites happening so that is why we hear about it much more than of anything else.
Now to dS. dS has a conformal infinity ("boundary"), but to evolve field theories in dS, we do not need to specify anything there! Actually, dS is the "anti" twin of AdS because dS in some sense needs the conformal infinity and generally far-away data less and less with evolution. Everything gets eventually devoured by the cosmological horizon, trajectories diverge, and matter (any field excitation with time-like/null behaviour) dilutes and stops interacting.
So, from this physical insight, I see very little prospect for a dS/CFT duality in the sense of a bulk-boundary theory. I do not know the work you cite but I would expect that the results for scalar field theory they get is a coincidence or a consequence of well chosen assumptions.
