Holographic Dual of de Sitter Universe with AdS Bubbles

TL;DR

This paper explores a holographic duality between a de Sitter universe with an AdS bubble and a boundary conformal field theory, deriving a formula for graviton absorption probabilities that depend on spacetime dimensions and localized graviton modes.

Contribution

It introduces a general formula for graviton absorption probability in d+1 dimensions and analyzes the role of localized gravitons and CFT degrees of freedom in this duality.

Findings

Absorption probability varies with even or odd spacetime dimensions.

Localized gravitons control the graviton absorption process.

The duality extends to a d-dimensional de Sitter universe with CFT matter.

Abstract

We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general $d+1$ spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of $d+1$ dimensional dS universe with an AdS bubble is also dual to a $d$ dimensional dS universe with CFT matter.