Abstract
In this paper we study various aspects of entanglement entropy in strongly- coupled de Sitter quantum field theories in various dimensions. We focus on 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.
Highlights
Quantum field theory in curved spacetimes [1, 2] is a subject of great relevance that has lead to many interesting areas of research in the past few decades
In this paper we have studied several properties of entanglement entropy in QFTs in de Sitter space, both in the static patch and the conformally flat patch
The theories in consideration have bulk duals coming from the standard Einstein-Hilbert action with negative cosmological constant and can be thought as models that belong to a universality class of strongly-coupled conformal field theory2 (CFT) in the large-N limit
Summary
Quantum field theory in curved spacetimes [1, 2] is a subject of great relevance that has lead to many interesting areas of research in the past few decades. Of particular relevance for the present context are the results of [69, 74] In these papers Liu and Suh showed that, for holographic theories with a gravity dual, entanglement entropy undergoes a series of regimes resembling those in phase transitions: pre-local-equilibration quadratic growth, post-local-equilibration linear growth, memory loss, and saturation. These results apply for strongly-coupled QFTs in Minkowski space. Is where holography plays a useful role This rest of the paper is organized as follows: in section 2, we study gravity solutions that are dual to field theories in a fixed de Sitter background.
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