Unitarity at infinity and topological holography

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. and others. The argument makes use of the unusual properties of gauge theories defined on topologically non-trivial spaces.