Pole skipping in two-dimensional de Sitter spacetime and double-scaled SYK model

Abstract

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation omega dS = i2 pi TdS(1 - s), where TdS = 1/2 pi L and s denotes spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon r = L for the scalar field of spin 0 and the fermionic field of spin 12 correspond one to one with those in the classical limit as lambda -> 0 in doublescaled Sachdev-Ye-Kitaev model when the temperature is infinite (DSSYK infinity). This provides a numerical correspondence between quantum gravity in the static patch of two-dimensional dS spacetime and a one-dimensional quantum system, which we consider as a realization of the DS/dS correspondence.