de Sitter Entanglement and Conformal Description of the Cosmological Horizon

TL;DR

This thesis explores the microscopic structure of the de Sitter cosmological horizon using orbifold geometries, Liouville theory, and holographic principles, revealing connections to conformal field theories and entanglement entropy.

Contribution

It introduces a novel approach linking orbifold geometries, Liouville theory, and dS/CFT correspondence to understand de Sitter horizons and entanglement.

Findings

Central charge matches Strominger's dS/CFT results

Proposes a quarter-area formula for entanglement entropy

Identifies conformal boundaries as codimension-two surfaces

Abstract

In this thesis, we aim to understand the microscopic details and origin of the Cosmological Horizon, produced by a static observer in four-dimensional de Sitter (dS$_4$) spacetime. We consider a deformed extension of dS spacetime by means of a single $\mathbb Z_q$ quotient, which resembles an Orbifold geometry. The Orbifold parameter induces a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. Using dimensional reduction on the two-dimensional plane where the minimal surfaces have support, we use the Liouville field theory and the Kerr/CFT mechanism in order to describe the underlying degrees of freedom of the Cosmological Horizon. We then show, that in the large $q$-limit, this pair of codimensions two surfaces can be realized as the conformal boundaries of dS$_3$. We notice that the central charge obtained using Liouville theory, in the latter limit, corresponds to the Strominger central charge obtained in the context of the dS/CFT correspondence. In addition, a formulation of entanglement entropy for de Sitter spacetimes is given in terms of dS holography and also a different approach in which the entanglement between two disconnected bulk observers is described in terms of the topology of the spacetime. Therefore, a quarter of the area formula is proposed, in which the area corresponds to the are of the set of fixed points of an $S^2/\mathbb Z_q$ orbifold.