Entanglement Entropy of Causal Set de Sitter Horizons

TL;DR

This paper investigates the entanglement entropy of causal set de Sitter horizons, demonstrating that an area law emerges under specific spectral truncations of the Pauli-Jordan operator, aligning with quantum gravity expectations.

Contribution

It extends the causal set approach to de Sitter horizons, showing how spectral truncation yields an area law for entanglement entropy in this context.

Findings

SSEE obeys an area law with spectral truncation in de Sitter slabs.

Without truncation, SSEE follows a volume law.

Truncation schemes can be chosen to enforce the area law.

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.