On “nothing” as an infinitely negatively curved spacetime

Abstract

Nothing-the absence of spacetime-can be either an endpoint of tunneling, as in the bubble of nothing, or a starting point for tunneling, as in the quantum creation of a universe. We argue that these two tunnelings can be treated within a unified framework, and that, in both cases, nothing should be thought of as the limit of anti-de Sitter space in which the curvature length approaches zero. To study nothing, we study decays in models with perturbatively stabilized extra dimensions, which admit not just bubbles of nothing-topology-changing transitions in which the extra dimensions pinch off and a hole forms in spacetime-but also a whole family of topology-preserving transitions that nonetheless smoothly hollow out and approach the bubble of nothing in one limit. The bubble solutions that are close to this limit, bubbles of next-tonothing, give us a controlled setting in which to understand nothing. Armed with this understanding, we are able to embed proposed mechanisms for the reverse process, tunneling from nothing to something, within the relatively secure foundation of the Coleman-De Luccia formalism and show that the Hawking-Turok instanton does not mediate the quantum creation of a universe.

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