de Sitter Entanglement and Conformal Description of the Cosmological Horizon

Felipe Diaz

paper

de Sitter Entanglement and Conformal Description of the Cosmological Horizon

arXiv:1911.06627

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 $Z_{q}$ 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 $S^{2} / Z_{q}$ orbifold.

arXiv comment107 pages, 12 figures, MSc thesis; based on arXiv:1901.04554, arXiv:1906.05310

de Sitter Entanglement and Conformal Description of the Cosmological Horizon

Abstract

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