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 $\omega_{dS}=i2\pi T_{dS}(1-s)$ with $T_{dS}$ denotes $T_{dS}=1/2\pi L$ 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-$\frac{1}{2}$ correspond one-to-one with those in the infinite temperature limit of double-scaled Sachdev-Ye-Kitaev model (DSSYK$_\infty$). 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 dS$_2$ spacetime and the DSSYK$_\infty$ model.