A Numerical Calculation of Entanglement Entropy in de Sitter Space

TL;DR

This paper numerically investigates how entanglement entropy of a scalar field in de Sitter space varies with key physical scales, revealing de Sitter corrections and finite-size effects.

Contribution

It provides the first high-precision numerical analysis of entanglement entropy in de Sitter space, including derivation of leading corrections and finite-size behavior.

Findings

De Sitter corrections to flat-space entanglement entropy are derived.

Finite-size effects show a logarithmic dependence on system size.

Sector with zero angular momentum contributes significantly to entropy.

Abstract

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.