Islands in Multiverse Models

TL;DR

The paper analyzes false-vacuum eternal inflation in two-dimensional JT gravity toy models by coupling a large‑c CFT and applying the island rule to compute the fine-grained entropy of subregions. It demonstrates a Page-like transition in which, for sufficiently large regions, a single island forms and covers most of the exterior multiverse, suggesting a strong coarse-graining of global structure in the semiclassical description. The results bridge JT multiverse island physics with semiclassical quantum cosmology, where local predictions arise from a small set of saddle geometries that average over large-scale eternal-inflation features. This inside-out viewpoint supports the idea that the global spacetime may be fundamentally reducible to localized patches with a controlled, coarse-grained description, potentially resolving aspects of the measure problem. The work also draws parallels to 4D quantum cosmology via the Hartle–Hawking wavefunction, highlighting a common thread: increased observational detail reveals new saddles or islands that encode global information in a localized, predictive framework.

Abstract

We consider multiverse models in two-dimensional linear dilaton-gravity theories as toy models of false vacuum eternal inflation. Coupling conformal matter we calculate the Von Neumann entropy of subregions. When these are sufficiently large we find that an island develops covering most of the rest of the multiverse, leading to a Page-like transition. This resonates with a description of multiverse models in semiclassical quantum cosmology, where a measure for local predictions is given by saddle point geometries which coarse-grain over any structure associated with eternal inflation beyond one's patch.

Figures (20)

• Figure 1: Penrose diagram for $\mathrm{dS}_2$. The horizontal line $\sigma = \pi/2$ corresponds to $\mathcal{I}^+$. The expanding patch (the past domain of dependence of the part of $\mathcal{I}^+$ where $\phi$ diverges to $+\infty$) is shaded in yellow, and the crunching patch (the past domain of dependence of the part of $\mathcal{I}^+$ where $\phi$ diverges to $-\infty$) is shaded in green.
• Figure 2: Penrose diagram for extended $\mathrm{dS}_2^n$. The case with $n=3$ is drawn here for illustration. The region $R$ lies in the expanding patch that is centered about $\varphi=0$. We take as an ansatz an island, $I$, whose endpoints $(\sigma_I, \pm \varphi_I)$ are in the crunching patches that are adjacent to $R$.
• Figure 3: (Left) Penrose diagram for $\mathbb{R}^{1,1}$. (Right) Penrose diagram for $\mathrm{dS}_2$ where the expanding patch has been replaced with a bubble of flat spacetime. The potion of full $\mathbb{R}^{1,1}$ that this bubble corresponds to is shaded in the left diagram.
• Figure 4: (Left) Penrose diagram for global $\mathrm{AdS}_2$. (Right) Penrose diagram for $\mathrm{dS}_2$ where the crunching patch has been replaced with a bubble of $\mathrm{AdS}_2$. The potion of the $\mathrm{AdS}_2$ manifold that this bubble corresponds to is shaded in the left diagram. Although not illustrated here, the diamond centred about $(\sigma',\varphi') = (0,\pi/2)$ could be used to replace the expanding patch of $\mathrm{dS}_2$.
• Figure 5: $S_\mathrm{CFT}(R)$ (brown, blue, dark green) versus $S_{\rm island}(R)$ (orange, red, black) in dS$^n_2$ for $n=1,\;2,\;+\infty$, respectively, with $\sigma_R =\pi/2-10^{-5}$ held fixed. The size of $R$ beyond which the island contribution to generalized entropy becomes dominant slightly decreases as $n$ increases. Because $\sigma_R$ is held fixed in this plot, taking $\varphi_R$ all the way to $\pi/2$ moves the endpoint of $R$ outside of the expanding patch. In this limit, the endpoint of $I$ also moves outside of the crunching patch and $R \cup I$ tends to a full Cauchy slice on which the state is pure, resulting in vanishing entropy. The parameter values used for this plot are $c = 600$, $\phi_r =10$, $\phi_0 =0$, $\epsilon_\mathrm{uv} = 1$, $\epsilon_\mathrm{rg} =1$.