Entanglement of Vacuum States With the de Sitter Horizon: Consequences on Holographic Dark Energy

TL;DR

This paper investigates how quantum entanglement between vacuum states near a de Sitter horizon relates to holographic dark energy, revealing that entanglement exists only within a few Planck lengths of the horizon and may influence the cosmological constant.

Contribution

It demonstrates that entanglement between vacuum states near the de Sitter horizon is limited to a few Planck lengths, providing insights into the quantum structure of horizons and dark energy.

Findings

Entanglement exists between vacuum states near the horizon within ~1 l_p.

Entanglement disappears beyond ~5 l_p from the horizon.

Horizon entanglement may impact the understanding of dark energy.

Abstract

The aim of this article is to study the effect of an Event Horizon on the entanglement of the Quantum Vacuum and how entanglement, together with the Holographic Principle, may explain the current value of the Cosmological Constant, in light of recent theories. Entanglement is tested for vacuum states very near and very far from the Horizon of a de Sitter Universe, using the Peres-Horodecki (PPT) criterion. A scalar vacuum field ($\hat{\phi}$) is averaged inside two boxes of volume $V$ in different spatial positions such that it acquires the structure of a bipartite Quantum Harmonic Oscillator, for which the PPT criterion is a necessary but not sufficient condition of separability. Entanglement is found between states obtained from boxes shaped as spherical shells with thickness of the order of one Planck distance ($l_p$), when one of the states is near the Horizon, and the other state is anywhere in the Universe. Entanglement disappears when the distance of the state near the horizon and the Horizon increases to around $5l_p$. If we consider the Horizon not as a surface but as a spherical shell of thickness $l_p$, then this means that there is entanglement between the states in the Horizon and the rest of the Universe. When both states are at distances larger than $\sim 5 l_p$ from the Horizon, no entanglement is found.