A Numerical Calculation of Entanglement Entropy in de Sitter Space

The entanglement entropy of a massless scalar field in de Sitter space depends on multiple scales, such as the radius of the entangling surface, the Hubble constant and the UV cutoff. We perform a high-precision numerical calculation using a lattice model in order to determine the dependence on these scales in the Bunch-Davies vacuum. We derive the leading de Sitter corrections to the flat-space entanglement entropy for subhorizon entangling radii. We analyze the structure of the finite-size effects and we show that the contribution to the entanglement entropy of the sector of the theory with vanishing angular momentum depends logarithmically on the size of the overall system, which extends beyond the horizon.