A New Approach to String Cosmology

TL;DR

The paper investigates how quotients of AdS space by discrete isometries can model cosmological spacetimes within the AdS/CFT framework. It analyzes boundary identifications, the challenges posed by dense fixed points, and proposes a method to define quotient states on the boundary CFT via induction from distributional AdS states, capturing linearized supergravity modes in the cosmology. A key contribution is a concrete construction using rigged Hilbert spaces to relate Γ-invariant AdS states to CFT states, yielding a manageable quotient Hilbert space for cosmological perturbations. The work lays groundwork toward a nonperturbative, potentially background-independent description of string cosmology, while acknowledging substantial open questions about interactions, winding sectors, and topology change.

Abstract

We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum size and then contract. Maldacena's conjecture suggests that they should be represented in string theory by suitable quotients of the boundary conformal field theory. We discuss the required identifications, and construct the states associated with the linearized supergravity modes in the cosmological background.