De Sitter Space and Entanglement

TL;DR

The paper investigates how de Sitter entropy can be understood as a consequence of spacetime entanglement, proposing a holographic picture where an inertial observer corresponds to a thermofield double across the two conformal boundaries. It develops a geometric framework with extended coordinates and dS_4/ Z_q orbifolds, yielding antipodal defects and spindle horizon structures. Entanglement entropies computed from boundary replicas and bulk orbifold fixed points reproduce the Gibbons–Hawking entropy via area laws, highlighting the role of both boundary and bulk topology. The work illuminates how replica symmetry and antipodal identifications arise from bulk symmetries and discusses implications for dS energy, AdS analogies, and multi-boundary generalizations.

Abstract

We argue that the notion of entanglement in de Sitter space arises naturally from the non-trivial Lorentzian geometry of the spacetime manifold, which consists of two disconnected boundaries and a causally disconnected interior. In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons--Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities. When considering the bulk entanglement between the two causally disconnected Rindler wedges, we show that the corresponding entanglement entropy is given by one quarter of the area of the pair of codimension two minimal surfaces that define the set of fixed points of the dS$_4/\mathbb Z_q$ orbifold.