Cosmology from random entanglement

TL;DR

The paper constructs a holographic model of a closed Λ<0 cosmology in AdS/CFT by coupling two AdS spacetimes through a heavy shell, yielding a bulk cosmology that is prepared via a Euclidean path integral. It shows that the cosmology can appear as an entanglement island in either boundary CFT and derives an island formula for the entropy using the FLM replica trick, with the cosmology in the entanglement wedge of one side depending on entanglement differences between the AdS regions. A central result is that the cosmology-to-boundary map is non-isometric in general, but may become approximately isometric for “simple” cosmological states once the AdS–cosmology entanglement exceeds a calculable threshold, a behavior illustrated in a tensor-network toy model. The authors also provide a state-dependent reconstruction of cosmology operators on the boundary and discuss the implications for holographic encoding, information recovery, and the operational distinguishability of cosmological states, laying groundwork for broader lessons about holographic cosmology and nonperturbative encoding.

Abstract

We construct entangled microstates of a pair of holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement of two disconnected auxiliary AdS spacetimes. We show that the island formula for the fine grained entropy of one of the CFTs follows from a standard gravitational replica trick calculation. In generic settings, the cosmology is contained in the entanglement wedge of one of the two CFTs. We then investigate properties of the cosmology-to-boundary encoding map, and in particular, its non-isometric character. Restricting our attention to a specific class of states on the cosmology, we provide an explicit, and state-dependent, boundary representation of operators acting on the cosmology. Finally, under genericity assumptions, we argue for a non-isometric to approximately-isometric transition of the cosmology-to-boundary map for ``simple'' states on the cosmology as a function of the bulk entanglement, with tensor network toy models of our setup as a guide.

Figures (23)

• Figure 1: Semiclassical state prepared by the gravitational path integral at low preparation temperatures. The geometry of the Euclidean section $X$ consists of two thermal AdS spaces. Each space has topology $\mathbf{D}^d\times \mathbf{S}^1$, where $\mathbf{D}^d$ is a $d$-dimensional ball, and $\mathbf{S}^1$ is the additional non-contractible thermal circle. The two solutions are glued together along the trajectory of the thin shell (red line). The Euclidean manifold $X$ is homotopic to a pair of pants. The semiclassical state is prepared on the time reflection-symmetric slice $\Sigma$ (blue slice), which contains the initial data of two global AdS timeslices $\Sigma_\mathsf{l}$ and $\Sigma_\mathsf{r}$, and a third closed universe $\Sigma_\mathsf{c}$ supported by the thin shell. In the Loretzian section, obtained from analytic continuation along $\Sigma$, the universe crunches towards the future.
• Figure 2: Schematic representation of the semiclassical state. The lines connecting the cosmology to the left and right AdS spacetimes represent entanglement between bulk fields. The green line cutting the entanglement lines represents the dominant RT surface for the whole CFT${}_\mathsf{L}$, which is geometrically empty. The cosmology $\mathsf{c}$ is contained within the entanglement wedge of CFT${}_\mathsf{L}$.
• Figure 3: TN model of our setup defining the cosmology-to-boundary map $V_\psi$.
• Figure 4: Euclidean path integral on the flat cylinder preparing $\ket{\Psi_{\mathcal{O}}}$.
• Figure 5: Semiclassical state prepared by the gravitational path integral at high preparation temperatures. The Euclidean section $X$ consists of two Euclidean black holes of masses $M_{\mathsf{L}}$ and $M_{\mathsf{R}}$. Each solution is topologically $\mathbf{D}^2 \times \mathbf{S}^{d-1}$, where $\mathbf{D}^2$ is a two dimensional disk (each point in the figure corresponds to a transverse $\mathbf{S}^{d-1}$). The two solutions are glued together along the worldvolume of the thin shell $\mathcal{W}$, in red. The semiclassical bulk state is prepared at the time reflection-symmetric slice $\Sigma$ (blue slice), which contains a long Einstein-Rosen bridge supported by the shell. In the Lorentzian section, the shell hides behind the horizon of the two-sided black hole.