Entanglement Entropy of Causal Set de Sitter Horizons

Abstract

de Sitter cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set de Sitter horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the causal set SSEE for the Rindler-like wedge of a symmetric slab of de Sitter spacetime in $d=2,4$ spacetime dimensions using the Sorkin-Johnston vacuum state. We find that the SSEE obeys an area law when the spectrum of the Pauli-Jordan operator is appropriately truncated in both the de Sitter slab as well as its restriction to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume law. This is in agreement with Sorkin and Yazdi's calculations for the causal set SSEE for nested causal diamonds in ${\mathbb{M}}^2$, where they showed that an area law is obtained only after truncating the Pauli-Jordan spectrum. In this work we explore different truncation schemes with the criterion that the SSEE so obtained obeys an area law.

arXiv comment30 pages, 16 figures

References in corpus (29)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement entropy of black holes
• The causal set approach to quantum gravity
• Horizon Entropy
• Entanglement entropy in de Sitter space
• Black hole entropy as entanglement entropy: a holographic derivation
• Black Hole Entropy and Induced Gravity
• De Sitter Holography and Entanglement Entropy
• Feynman Propagator for a Free Scalar Field on a Causal Set
• Particle propagators on discrete spacetime
• A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
• Large Fluctuations in the Horizon Area and what they can tell us about Entropy and Quantum Gravity
• Entanglement Entropy in Causal Set Theory
• Adventures in de Sitter space
• Gravitation and vacuum entanglement entropy
• Black hole entanglement entropy and the renormalization group
• A Ground State for the Causal Diamond in 2 Dimensions
• What is mass in desitterian physics?
• From Green Function to Quantum Field
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Spacetime Entanglement Entropy in 1+1 Dimensions
• Studies on the SJ Vacuum in de Sitter Spacetime
• Scalar Field Green Functions on Causal Sets
• When is an area law not an area law?
• On the Entanglement Entropy of Quantum Fields in Causal Sets
• The Sorkin-Johnston State in a Patch of the Trousers Spacetime
• Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond

Cited by in corpus (9)

• Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Spacetime Entanglement Entropy: Covariance and Discreteness
• Everything You Always Wanted to Know About How Causal Set Theory Can Help with Open Questions in Cosmology, but Were Afraid to Ask
• Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons
• Entanglement Entropy and Causal Set Theory
• Aspects of Quantum Fields on Causal Sets
• On the (Non)Hadamard Property of the SJ State in a $1+1$D Causal Diamond
• Discrete Black Holes