# de Sitter entropy as entanglement

## TL;DR

This paper explores extremal surfaces in de Sitter space and proposes a duality with entangled ghost-like conformal field theories, providing insights into de Sitter entropy and entanglement structure.

## Contribution

It introduces connected timelike extremal surfaces in de Sitter space and suggests a novel duality with entangled ghost CFTs, extending the holographic framework.

## Key findings

- Existence of extremal surfaces connecting future and past boundaries in de Sitter space.
- Proposal of a duality between de Sitter space and entangled ghost CFTs.
- Positive norm and entanglement in ghost-spin systems support the duality concept.

## Abstract

We describe connected timelike codim-2 extremal surfaces stretching between the future and the past boundaries in the static patch coordinatization of de Sitter space. These are analogous to rotated versions of certain surfaces in the $AdS$ black hole. The existence of these surfaces via the $dS/CFT$ framework suggests the speculation that $dS_4$ is dual to two copies of ghost-like CFTs in a thermofield-double-type entangled state. In studies of entanglement in ghost systems and "ghost-spin" chains, we show that similar entangled states in two copies of ghost-spin ensembles always have positive norm and positive entanglement.