Fluctuations and non-Gaussianity in de Sitter spacetime from holographic entanglement entropy

TL;DR

This paper investigates fluctuations and non-Gaussian features in de Sitter spacetime using holographic entanglement entropy, revealing their significance during the primordial era and their impact on spacetime geometry.

Contribution

It demonstrates that de Sitter spacetime fluctuates due to entanglement entropy, with a detailed analysis of the fluctuations' distribution and their backreaction on the geometry.

Findings

Fluctuations of entanglement entropy backreact on the bulk geometry.

Variance of fluctuations is suppressed by Newton's constant and scaled by the Hubble parameter.

Distribution of fluctuations exhibits skewness with a non-linearity parameter of order one.

Abstract

Using entanglement in dS/CFT correspondence, we show that a 4-dimensional de Sitter spacetime in the bulk fluctuates. We calculated the fluctuations of the entanglement entropy, which backreacts with the geometry of the bulk spacetime indicated by the fluctuations of the horizon radius. The variance of the fluctuations is suppressed by $G_N$ and multiplied by $H_{dS}^2$. Therefore, it will be more significant during the primordial era where it is also well described by de Sitter geometry. We also show that the distribution of the fluctuations is also skewed with the local non-linearity parameter is in the order of $f_{NL}\sim\mathcal{O}(1)$ and we present the probability density function with corrections up to $\sigma_\Phi^3$.