# De Sitter Space and Entanglement

## TL;DR

This paper explores how entanglement in de Sitter space naturally emerges from its Lorentzian geometry, proposing a holographic framework linking entanglement entropy to geometric features like minimal surfaces.

## Contribution

It introduces a holographic description of entanglement in de Sitter space, connecting the Gibbons-Hawking entropy to entanglement entropy between boundaries and wedges.

## Key findings

- Holographic entanglement entropy matches Gibbons-Hawking formula.
- Entanglement entropy between causally disconnected regions is proportional to minimal surface area.
- Proposes a tensor product structure for the Hilbert space of an inertial observer.

## Abstract

We argue that the notion of entanglement in de Sitter space arises naturally from the non-trivial Lorentzian geometry of the spacetime manifold, which consists of two disconnected boundaries and a causally disconnected interior. In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons--Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities. When considering the bulk entanglement between the two causally disconnected Rindler wedges, we show that the corresponding entanglement entropy is given by one quarter of the area of the pair of codimension two minimal surfaces that define the set of fixed points of the dS$_4/\mathbb Z_q$ orbifold.