Pole-skipping in the de Sitter horizon structure

TL;DR

This paper investigates the pole-skipping phenomenon at the cosmic horizon in de Sitter spacetime, revealing that various fields share the same pole-skipping frequencies as in anti-de Sitter space, with shifts in momenta due to curvature.

Contribution

It demonstrates that pole-skipping points for different spins in de Sitter space have the same frequencies as in AdS, with a curvature-induced shift in momenta, linking operator dimensions across curved spacetimes.

Findings

Pole-skipping frequencies are identical for various spins in dS and AdS.

Momentums at pole-skipping points are shifted due to spacetime curvature.

Momentum conjugates are complex in dS and AdS, reflecting opposite curvatures.

Abstract

We study the pole-skipping structure of incoming waves near the cosmic horizon $r=r_c$ in de Sitter (dS) spacetime. We find that the scalar field with spin-0, the Dirac field with spin-1/2, the Maxwell field with spin-1, the Rarita-Schwinger field with spin-3/2, and the gravitational field with spin-2 exhibit the same frequencies $\omega_\star$ of pole-skipping points as their corresponding spin fields satisfying the incoming wave conditions in anti-de Sitter (AdS) spacetime. However, the momenta $k_\star$ undergo a shift in complex space, which originates from the spacetime curvature. The shift in momenta at the pole-skipping points could be measured through the operator dimensions $\Delta$ in two curved spacetimes, where momenta are mutually complex conjugate in dS and AdS, two opposite curvature spacetimes.