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

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 $\sigma_\Phi^3$.