Cosmology from random entanglement

TL;DR

This paper constructs entangled states of holographic CFTs that encode big bang-big crunch cosmologies in AdS spaces, analyzing their entanglement structure, boundary encoding, and transition from non-isometric to isometric mappings.

Contribution

It introduces a novel construction of cosmological states in holography, explores their entanglement properties, and examines the boundary encoding map's transition behavior.

Findings

Cosmologies are supported by inhomogeneous matter in entangled CFT states.

The island formula for entropy is derived via a gravitational replica trick.

The cosmology-to-boundary map transitions from non-isometric to approximately-isometric with increasing entanglement.

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.