Unitarity at Infinity and Topological Holography

TL;DR

This paper explores the implications of unitarity and topological properties in the context of the dS/CFT correspondence, suggesting a non-singular origin of the universe and analyzing constraints on bulk matter fields.

Contribution

It proposes a novel interpretation of the Strominger bound as related to the matter equation of state and discusses the universe's potential non-singular origin via topological gauge theories.

Findings

The Strominger bound reflects the cosmological matter equation of state.

The universe may originate from a non-singular spacelike hypersurface.

Topologically non-trivial gauge theories are relevant to cosmological models.

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.