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 , 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.

众所周知，德西特 (dS) 宇宙视界表现出类似于黑洞视界的热力学特性。在这项工作中，我们使用 Sorkin 的时空纠缠熵 (SSEE) 公式研究了共形耦合量子标量场的因果集 dS 视界。我们使用 Sorkin-Johnston 真空态计算d = 2, 4 时空维度中 dS 时空对称板的类林德勒楔形的因果集 SSEE 。我们发现，当 Pauli-Jordan 算子的频谱在 dS 板及其对 Rindler 类楔形的限制中被适当截断时，SSEE 遵守面积定律。如果没有这种截断，SSEE 满足体积定律。这与 Sorkin 和 Yazdi 对嵌套因果钻石的因果集 SSEE 的计算一致，他们表明只有在截断 Pauli-Jordan 谱后才能获得面积定律。在这项工作中，我们以这样获得的 SSEE 遵循面积定律为标准，探索了不同的截断方案。