  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.
