The Multiverse in an Inverted Island

TL;DR

This work analyzes redundancies in the global spacetime description of the eternally inflating multiverse using the quantum extremal surface framework. It shows that for a sufficiently large subregion $R$ within a bubble, an inverted island $I$ forms that surrounds the bubble, so the semiclassical multiverse dynamics are encoded in the finite degrees of freedom on the complement of $I$ on a Cauchy surface. The formation of the inverted island relies on bulk entanglement generated by Unruh radiation from accelerating domain walls and collisions with surrounding collapsing AdS bubbles, leading to a reduction of the generalized entropy $S_{\rm gen}$ and the existence of a quantum extremal surface. This construction provides a potential resolution to the cosmological measure problem by replacing infinite degrees of freedom with a finite, holographically anchored description on an effective Cauchy surface, and it suggests a broader holographic program for cosmology via finite-region holography.

Abstract

We study the redundancies in the global spacetime description of the eternally inflating multiverse using the quantum extremal surface prescription. We argue that a sufficiently large spatial region in a bubble universe has an entanglement island surrounding it. Consequently, the semiclassical physics of the multiverse, which is all we need to make cosmological predictions, can be fully described by the fundamental degrees of freedom associated with certain finite spatial regions. The island arises due to mandatory collisions with collapsing bubbles, whose big crunch singularities indicate redundancies of the global spacetime description. The emergence of the island and the resulting reduction of independent degrees of freedom provides a regularization of infinities which caused the cosmological measure problem.

Figures (7)

• Figure 1: The multiverse as an entanglement castle. On a given Cauchy surface $\Xi$, the physics of the multiverse can be described by the fundamental degrees of freedom associated with the region $R \cup (\overline{R \cup I_\Xi})$, where $I_\Xi = D(I) \cap \Xi$ with $I$ being the (inverted) island of a partial Cauchy surface $R$.
• Figure 2: A sketch of the Penrose diagram of the multiverse. We focus on an arbitrarily chosen bubble, which we call the central bubble. The central bubble is nucleated in a parent dS bubble and is surrounded by collapsing AdS bubbles which collide with it at late times.
• Figure 3: Generation of $S_{\rm bulk}$ by an accelerating domain wall. The blue and red lines are entanglement partners of each other. This results in the region $A$, shown in green, to have a large $S_{\rm bulk}$.
• Figure 4: Penrose diagram showing the region near the domain wall (yellow strip) separating the central dS/Minkowski and surrounding AdS bubbles at late times. The transverse directions corresponding to the hyperboloid $H_2$ have been suppressed. $\partial \Sigma'$ is a boundary of a partial Cauchy surface $\Sigma'$ and $k^\mu$, $l^\mu$ are future-directed null vectors orthogonal to it. Blue and red arrows indicate Unruh radiation and their partner modes, respectively, and the double line at the top of the AdS bubble represents the big crunch singularity. The signs of classical expansions $\theta_{k,l}$ are shown in green following the Bousso wedge convention Bousso:1999xy.
• Figure 5: A sketch of the construction of closed codimension-2 surface $\partial I'$. The central bubble and some of the surrounding AdS bubbles are depicted as the green and blue cones, respectively. The region $I'$ is defined as a partial Cauchy surface bounded by and outside $\partial I'$.