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

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation ωdS=i2π TdS(1-s) with TdS denotes TdS=1/2π L and s 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-1/2 correspond one-to-one with those in the infinite temperature limit of double-scaled Sachdev-Ye-Kitaev model (DSSYK_∞). The retarded Green's functions of these two systems also have similar forms at the pole-skipping positions. This provides a numerical correspondence between the static patch of dS₂ spacetime and the DSSYK_∞ model.