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 $\omega_{dS}=i2\pi T_{dS}(1-s)$, where $T_{dS}=1/2\pi L$ 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-$\frac{1}{2}$ correspond one-to-one with those in the classical limit as $\lambda\rightarrow 0$ in double-scaled Sachdev-Ye-Kitaev model when the temperature is infinite (DSSYK$\infty$). This provides a numerical correspondence between the static patch of two-dimensional dS spacetime and the DSSYK$\infty$ model. We present that the dimensionless parameter $\beta\mathcal{J}$\textendash encoding the interplay between temperature and interaction energy\textendash serves as a universal scaling factor governing the pole-skipping structure in the SYK model. The pole-skipping points undergo a transition from correspondence with dS spacetime at $\beta\mathcal{J}\rightarrow 0$ to Anti-de Sitter (AdS) spacetime at $\beta\mathcal{J}\rightarrow \infty$.