# Entropy, Entanglement and Swampland Bounds in DS/dS

## TL;DR

This paper explores the entanglement entropy in de-Sitter space using the DS/dS correspondence, revealing multiple minimal surfaces and their implications for entropy bounds and the swampland conjecture.

## Contribution

It identifies a family of bulk minimal surfaces calculating dS entropy and analyzes their physical interpretations and implications for entropy bounds and the swampland.

## Key findings

- Multiple minimal surfaces with the same area exist in dS space.
- Some surfaces represent entanglement between dual CFTs, others across the horizon.
- Entanglement entropy with extra matter exceeds the dS entropy.

## Abstract

We calculate the entanglement entropy of the de-Sitter (dS) static patch in the context of the DS/dS correspondence. Interestingly, we find that there exists a one parameter family of bulk minimal surfaces that all have the same area. Two of them have appeared earlier in the literature. All of them correctly calculate the dS entropy. One surface yields the entanglement between the two different CFTs that provide the holographic dual of the bulk DS geometry. The second surface describes the entanglement across the horizon in the boundary static patch. The other surfaces describe a mixture of these two concepts. We also show that in the presence of extra matter fields the former entanglement entropy always exceeds the dS entropy. We interpret this result in the context of entropy bounds in de Sitter space and the swampland program.