A Holographic Framework for Eternal Inflation

TL;DR

The authors propose a local holographic dual for eternal inflation built from Coleman-De Luccia bubble nucleation, positing a 2D Euclidean CFT living on the open FRW boundary Sigma with a Liouville field encoding emergent boundary time. By analyzing scalar and graviton correlators in the CDL geometry and performing analytic continuation to the boundary, they identify a tower of definite-dimension boundary operators and a dimension-2 stress-tensor-like piece, while non-normalizable modes imply a dynamical boundary geometry. They then flesh out a framework where a Wheeler-DeWitt wavefunction is recast as a boundary action S(L,f) defining a 2D CFT on Sigma, introducing a holographic-WDW theory with potential locality and a boundary time linked to Liouville dynamics. Nonperturbative boundary effects, such as bubble collisions and instantons, are interpreted as boundary instantons encoding the Landscape, suggesting a rich, albeit non-unitary, holographic description of the multiverse. Open questions remain on the locality, UV structure, and complete operator content of the boundary theory, as well as how to fully realize the Landscape within this holographic WDW framework.

Abstract

In this paper we provide some circumstantial evidence for a holographic duality between bubble nucleation in an eternally inflating universe and a Euclidean conformal field theory. The holographic correspondence (which is different than Strominger's dS/CFT duality) relates the decay of (3+1)-dimensional de Sitter space to a two-dimensional CFT. It is not associated with pure de Sitter space, but rather with Coleman-De Luccia bubble nucleation. Alternatively, it can be thought of as a holographic description of the open, infinite, FRW cosmology that results from such a bubble. The conjectured holographic representation is of a new type that combines holography with the Wheeler-DeWitt formalism to produce a Wheeler-DeWitt theory that lives on the spatial boundary of a k=-1 FRW cosmology. We also argue for a more ambitious interpretation of the Wheeler-DeWitt CFT as a holographic dual of the entire Landscape.

Figures (7)

• Figure 1: Penrose diagram for the Lorentzian continuation of the CDL instanton. Region I is an open ($k=-1$) FRW universe which is asymptotically flat. Region IV is asymptotically de Sitter. $\Sigma$ is the conformal 2-sphere defined by the intersection of the light-like infinity of region I and the space-like infinity of region IV. The curves indicate orbits of the $SO(3,1)$ symmetry, which acts on $\Sigma$ as the conformal group.
• Figure 2: (a) Contour surrounding single poles at $k=2i,3i,\ldots$. (b) Coutour surrounding a double pole at $k=i$, single poles at $k=0,-2i,-3i,\ldots$, and a single pole at $k=-ia$$(0<a<1)$ which is due to the pole of ${\cal R} (k)$; for the "half-sphere" example in Appendix A.2, $a=1/2$. There is no pole at $k=-i$ since ${\cal R} (k)$ has a zero there.
• Figure 3: Top: Time-like trajectory that ends up in a bubble. Bottom: Time-like trajectory that meets a flat-space bubble at $\Sigma$. Since infinitely many bubbles, which are not drawn here, form in de Sitter space, this trajectory will inevitably be caught in another bubble like the one in the top figure.
• Figure 4: Collision of two flat-space bubbles of different types.
• Figure 5: A red instanton inside a blue instanton.