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

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.

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