Entanglement entropy of causal set de Sitter horizons

Abstract

de Sitter (dS) cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set dS 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 dS 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 dS 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