Finite complexity of the de Sitter vacuum

TL;DR

This paper investigates the complexity of the de Sitter vacuum under the ER=EPR conjecture, finding it to be finite and suggesting universal features of spacetime entanglement and thermalization.

Contribution

It extends the ER=EPR framework to de Sitter space, demonstrating the finiteness of vacuum complexity and proposing implications for cosmic entanglement and thermalization.

Findings

Complexity per volume of the de Sitter vacuum is finite in UV and IR.

Supports the universality of entanglement features in spacetimes with horizons.

Provides evidence for cosmic ER=EPR and insights into quantum thermalization.

Abstract

The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter spacetimes, its implications for an accelerating universe, such as our own, remain less explored. Assuming a cosmic version of ER=EPR for de Sitter space, we explore computational complexity corresponding to long-range entanglement responsible for bulk states on spacelike hypersurfaces. Rather remarkably, we find that the complexity (per unit volume) of the Euclidean vacuum, as an entangled state over two boundary CFT vacua, is finite both in the UV and the IR, which provides additional evidence for cosmic ER=EPR. Our result seems to be a universal feature of spacetimes with horizons and, moreover, hints at new features of the thermofield double state for studying thermalization of any quantum system.