Entanglement entropy in FRW backgrounds

TL;DR

This paper uses holography to analyze entanglement entropy in FRW cosmological backgrounds, accounting for arbitrary scale factor evolution, spatial curvature, and finite temperature effects, providing new insights into quantum entanglement in dynamic spacetimes.

Contribution

It introduces a coordinate transformation method to compute entanglement entropy in time-dependent FRW backgrounds, extending previous static analyses and including finite temperature and curvature effects.

Findings

Agreement with known entanglement entropy forms

Finite terms related to expansion rate in 4D

Method applicable to various dimensions and curvatures

Abstract

We use holography in order to study the entanglement entropy for a spherical entangling surface in a FRW background with an arbitrary time dependence of the scale factor. The calculation is done in various dimensions, allowing for nonzero spatial curvature. The entanglement entropy of a CFT at nonzero temperature in this background is also considered. Our approach is based on coordinate transformations that relate the extremization problem to the one for a static background, with a careful determination of the UV cutoff. We demonstrate the agreement with the expected form of the entanglement entropy and with various known results in specific cases. In four dimensions, apart from the cutoff-dependent terms, we compute and discuss the finite term related to the expansion rate.