# The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes Source: [The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes]() Collection index: [llms.txt]() Data updated: 2025-10-25T08:40:04.553Z Authors: K. Andrzejewski Published: 2025-05-05T16:44:19.000Z ## Abstract We study the area and volume laws for entanglement of free quantum scalar fields. In addition to the entropy, we use the notion of the capacity of entanglement, which measures entropy fluctuations. We consider flat spacetimes as well as the curved ones relevant for cosmology. Moreover, we put special emphasis on quench phenomena and different geometries of the entangling surfaces. First, we show that, in the Minkowski spacetime, the capacity of entanglement, like entropy, exhibits the area law for two kinds of geometries of the entangling surfaces: the sphere and strip. Moreover, we show that the ratio of both quantities takes the same values for both surfaces. Next, we turn our attention to quenches. Namely, we analyse the dynamics of capacity; in particular, contribution of the volume and surface terms. Moreover, we compare these results with theoretical predictions resulting from the quasiparticles model. In the second part, we consider the above issues for the FLRW spaces; especially, for de Sitter space as well as a metric modeling the transition to radiation-dominated era. Finally, we analyse the abrupt quenches in de Sitter space. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()