Holographic de Sitter Universe

TL;DR

This paper explores embedding de Sitter space into five-dimensional anti-de Sitter space to calculate physical quantities like energy and entropy using the AdS/CFT correspondence, linking cosmological models with holographic principles.

Contribution

It introduces a novel approach to embed various de Sitter spaces into AdS5 for holographic analysis, including static, global, and inflationary cases, extending to general cosmology.

Findings

De Sitter space can be embedded into AdS5 to compute energy and entropy.

dS entropy can be interpreted as entanglement entropy in the AdS framework.

The approach extends to general cosmology with a positive cosmological constant, despite singularities.

Abstract

We propose to embed de Sitter space into five dimensional anti-de Sitter space to compute some physical quantities of interest, using the AdS/CFT correspondence. The static de Sitter can be considered as the conformal structure of the boundary of the hyperbolic AdS5 with a horizon, thus energy as well as entropy can be computed. The global dS can be embedded into a half-global AdS5, and the dS entropy can be regarded as entanglement entropy in this case. Finally, the inflationary dS can also be regarded as the boundary of AdS5, and this can be extended to include general cosmology with a positive cosmological constant, however at the price of introducing a naked null singularity in the bulk unless the cosmology is pure de Sitter space.