The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes

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.