Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs

TL;DR

The paper addresses how entanglement structure and non-equilibrium dynamics of strongly coupled quantum field theories in de Sitter space are encoded holographically. It constructs gravity duals with dS slices (static and conformally flat) and analyzes both equilibrium entanglement entropy and out-of-equilibrium evolution using Vaidya-type hyperbolic black holes. Key contributions include analytic results for (1+1) and (2+1) dimensions, a horizon-radius phase transition in entanglement entropy, a horizon-driven structure in renormalized entanglement entropy, and a detailed characterization of holographic thermalization with saturation times tied to light-crossing, suggesting free light-like degrees of freedom. Collectively, these results illuminate how curvature and cosmological horizons shape non-local quantum information measures and provide benchmarks for non-equilibrium dynamics in strongly coupled de Sitter QFTs.

Abstract

In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situations in which the system evolves from a non-equilibrium state to the Bunch-Davies state. We find that the saturation time is equal to the light-crossing time of the sphere. This behavior is faster than random walk and suggests the existence of free light-like degrees of freedom.

Figures (10)

• Figure 1: The total system can be divided into two subsystems A and $B\equiv A^c$; the entanglement entropy measures the amount of information loss because of smearing out in region B.
• Figure 2: A schematic diagram of the extremal surface used for calculation of the entanglement entropy.
• Figure 3: The two disjoint sub-systems $A$ and $B$, each of length $l$ along $X$-direction and separated by a distance $x$. The schematic diagram on the right shows the possible candidates for minimal area surfaces which is relevant for computing $S_{A\cup B}$. See Fischler:2012uv for a detailed discussion.
• Figure 4: Extremal surfaces for $d=2$ in $(r,z)$ coordinates; $zH=0$ is the boundary and $zH=2$ is the Killing horizon. Blue lines are U-shaped extremal surfaces for $lH<2$ and red lines are disconnected extremal surfaces for $lH>2$. Dashed brown line is the extremal surface for $lH = 2$.
• Figure 5: Entanglement/disentanglement transition of mutual information in $(1+1)-$dimensions. Mutual information is nonzero only in the shaded region. Dashed black line is the transition curve in flat space.