Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons

TL;DR

This paper investigates pole-skipping phenomena in de Sitter spacetimes, revealing connections to quantum chaos, horizon dynamics, and proposing dual field theories with nonlocal and non-Hermitian features.

Contribution

It systematically analyzes pole-skipping for various fields in de Sitter space, extracting chaos parameters, and proposes dual models with novel nonlocal and non-Hermitian properties.

Findings

Pole-skipping points constrain bulk two-point functions.

Lyapunov exponent and butterfly velocities match shock wave calculations.

Dual theories may involve entangled sectors with nonlocal and non-Hermitian characteristics.

Abstract

We present a systematic analysis of pole-skipping for scalar, Maxwell, and gravitational waves in cosmological spacetimes. Specifically, working in empty de Sitter space and in Schwarzschild-de Sitter black hole geometries, we locate the tower of pole-skipping points of such fields and show that they impose nontrivial constraints on the corresponding bulk two-point functions. Focusing on the gravitational sound channel, we then extract the Lyapunov exponent and butterfly velocities that characterize hypothetical dual many-body quantum chaos at each horizon. These chaotic data precisely match the outcome of a gravitational shock wave calculation, confirming that the relevant pole-skipping points encode high-energy scattering of horizon quanta. Interestingly, the butterfly velocities can become superluminal or imaginary, with the latter signaling a spatially modulated propagation of chaos. Assuming that a holographic dual exists, we translate our results into field theory language and propose that the dual theory can be divided into two entangled sectors that capture the black hole and cosmological horizon degrees of freedom. Our results suggest that the black hole sector becomes increasingly nonlocal as the black hole shrinks and that the cosmological horizon sector exhibits behavior compatible with violations of Hermiticity. Finally, we outline simple microscopic toy models, built from long-range and non-Hermitian deformations of the Double Scaled Sachdev-Ye-Kitaev (DSSYK)-type chains, that realize these features, providing a concrete arena for future exploration.