On scrambling, tomperature and superdiffusion in de Sitter space

This paper investigates basic properties of the de Sitter static patch using simple two-point functions in the probe approximation. We find that de Sitter equilibrates in a superdiffusive manner, unlike most physical systems which equilibrate diffusively. We also examine the scrambling time. In de Sitter, the two-point functions of free fields do not decay for sometime because quanta can reflect off the pole of the static patch. This suggests a minimum scrambling time of the order $\log(1/G_N)$, even for perturbations introduced on the stretched horizon, indicating fast scrambling inside de Sitter static patch. We also discuss the interplay between thermodynamic temperature and inverse correlation time, sometimes called "tomperature".