Unitarity at Infinity and Topological Holography

Abstract

Recently it has been suggested that non-gaussian inflationary perturbations can be usefully analysed in terms of a putative dual gauge theory defined on the future conformal infinity generated by an accelerating cosmology. The problem is that unitarity of this gauge theory implies a strong constraint [the "Strominger bound"] on the matter fields in the bulk. We argue that the bound is just a reflection of the equation of state of cosmological matter. The details motivate a discussion of the possible relevance of the ``dS/CFT correspondence" to the resolution of the Big Bang singularity. It is argued that the correspondence may require the Universe to come into existence along a non-singular spacelike hypersurface, as in the theories of ``creation from nothing" discussed by Firouzjahi, Sarangi, and Tye, and also by Ooguri et al. The argument makes use of the unusual properties of gauge theories defined on topologically non-trivial spaces.