Long-range correlation of CMB temperature fluctuations from the holographic entanglement entropy

TL;DR

This paper explores the connection between holographic entanglement entropy and cosmic microwave background (CMB) temperature fluctuations, proposing a novel framework to analyze quantum cosmological phenomena through entanglement correlations.

Contribution

It introduces a method to relate holographic entanglement entropy fluctuations to CMB temperature fluctuations using a new correlation function approach.

Findings

Holographic entanglement entropy perturbations follow a Gaussian distribution.

The entanglement entropy fluctuations correlate with CMB temperature anisotropies.

Distribution of entangling region sizes matches observed CMB multipole data.

Abstract

In this paper, we define the holographic multipartite entanglement entropy for $N$ separated subsystems living in a compact $\text{CFT}_d$ space-time. In a large $N$ limit, we find that the first-order holographic entanglement entropy perturbation is proportional to the change in the length of the subsystem and it has symmetric (Gaussian) distribution property. From that finding, we propose to construct two-point correlation functions of holographic entanglement entropy fluctuations analogous to the one that is used in the cosmic microwave background (CMB) temperature fluctuations analysis. Using the first law of thermodynamics, we may correlate tiny changes in entanglement entropy with the temperature fluctuations. By comparing with Planck 2018 CMB data from $j=2$ to $j=2499$ where $j$ denotes the multipole moment, we extract the distribution of the entangling region size that corresponds to the temperature fluctuations. Since the distribution of the entangling region size can be interpreted as the CMB temperature fluctuations, we conclude that entanglement might play a role in the quantum aspects of cosmology.