Toward a Consistent Definition of Holographic Entanglement Entropy in de Sitter Space

TL;DR

This paper proposes a new, consistent definition of holographic entanglement entropy in de Sitter space, addressing previous issues with the Ryu-Takayanagi prescription by enforcing entropic inequalities.

Contribution

It introduces a novel entropy functional for de Sitter space using the replica trick, ensuring compatibility with entropic inequalities and constraining static patch holography.

Findings

The new entropy functional satisfies strong subadditivity.

Entropic inequalities restrict the parameter space of static patch holography.

Results support static patch holography as a consistent de Sitter holographic framework.

Abstract

We investigate a new definition of holographic entanglement entropy in the framework of static patch holography for de Sitter space. Using the replica trick and twist operator formalism, we derive an entropy functional in three-dimensional de Sitter space expressed through de Sitter Green's functions. Since the naive Ryu-Takayanagi prescription in de Sitter spacetime fails to satisfy strong subadditivity, we demand that our proposed formula be consistent with the fundamental entropic inequalities. The resulting conditions place nontrivial constraints on the undetermined parameter space of static patch holography. Our results demonstrate that entanglement inequalities provide a sharp diagnostic for candidate definitions of entanglement entropy in de Sitter holography and offer quantitative evidence in support of static patch holography as a consistent framework.