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.

30 pages, 16 figures

References in corpus (8)

• Black hole entropy as entanglement entropy: a holographic derivation
• Feynman Propagator for a Free Scalar Field on a Causal Set
• Particle propagators on discrete spacetime
• Gravitation and vacuum entanglement entropy
• Adventures in de Sitter space
• Black hole entanglement entropy and the renormalization group
• What is mass in desitterian physics?
• The Sorkin-Johnston State in a Patch of the Trousers Spacetime

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