Calculation of the cosmological constant using the holographic principle

Abstract

The aim of this Thesis is to study the e ect 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. The states are averaged inside two boxes of volume V so that they acquire the structure of a bipartite Quantum Harmonic Oscillator, for which the PPT criterion is a necessary but not su cient condition of separability. The rst chapters are an introduction to: the Quantum Vacuum and its physical manifestation, quantum entanglement and its application to Gaussian States and Quantum Harmonic Oscillators, the Holographic Principle, the relation between entanglement and the Holographic Principle, theories developed to calculate the Cosmological Constant, and the experimental methods used to measure it. Entanglement was found between states averaged inside spherical shells with thickness of the order of one Planck distance (lp), 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 a value somewhere between 10lp and 60lp, or, in other words, when the state is at distances larger than O(10lp) to the Horizon. If we consider the Horizon not as a surface but as a spherical shell of thickness lp, 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 60lp from the Horizon, no entanglement was found.