The Boundary Proposal

TL;DR

The Boundary Proposal extends the traditional no-boundary framework by allowing a spacelike end-of-the-world brane to create a boundary-free de Sitter sphere from nothing, potentially dominating the LV tunneling channel when brane tension is negative or vanishes. The authors construct a new Euclidean instanton consisting of a sphere with two ETW branes, which can be glued to a Lorentzian de Sitter patch to realize a universe with a single initial boundary, and they provide a minisuperspace path-integral treatment to derive saddle-point amplitudes and wavefunctions. They analyze creation rates across three instanton geometries, showing that under LV sign the boundary process can dominate for negative or zero tension, while the no-boundary process remains dominant under the Hartle-Hawking sign; they also find that zero-tension ETW branes can yield a zero-action torus-universe from nothing. A notable implication is that toric universes with zero cosmological constant can be nucleated without exponential suppression, inviting further exploration of spacelike ETW branes, their fluctuations, and their embedding in string/M-theory contexts, as well as potential connections to other creation scenarios. The work thus opens new avenues for initial-condition cosmology and the string landscape, highlighting the role of brane tension and sign choices in determining the dominant origin of universes.

Abstract

One of the leading ideas for the beginning of the Universe is the Hartle-Hawking `No-Boundary Proposal.' Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider a `Boundary Proposal'. Specifically, the corresponding euclidean instanton is a sphere with two holes around north and south pole cut out. Analogously to the Hartle-Hawking proposal, the sphere is then cut in two at the equator and half of it is dropped. The equator is glued to an expanding Lorentzian de Sitter space, implementing a beginning of the Universe with a spacelike spherical boundary at its earliest moment. This process is in principle on equal footing with the one based on the no-boundary instanton. In fact, if the Linde-Vilenkin sign choice is used, this `Boundary' creation process may even dominate. An intriguing implication arises if tensionless end-of-the-world branes, as familiar from type-IIA or M-theory, are available: Analogously to the Boundary Proposal, one may then be able to create a compact, flat torus universe from nothing, without any exponential suppression or enhancement factors.

Figures (2)

• Figure 1: Illustration of the 'Swiss Cheese Instanton'.
• Figure 2: The spacetime geometry of a toric universe nucleating from nothing.