A de Sitter Anti-Scrambling Algebra
arXiv:2607.13665
The paper analyzes the algebra of observables for a semiclassical observer in de Sitter space, showing how shockwave scattering near the horizon affects out-of-time-ordered correlators and leads to a breakdown of the KMS condition and a non‑trace Hartle‑Hawking state, ultimately suggesting a trivial commutant and a free product algebra after the scrambling time.
Abstract
We study the algebra of observables of a semiclassical observer in de Sitter space. When operators are time-evolved by a scrambling time, out-of-time-ordered correlation functions (OTOCs) receive corrections due to shockwave scattering near the cosmological horizon. When the observer's clock is treated classically, we show that the time advance effect implies the breakdown of the KMS condition for vacuum correlators of matter operators. When the observer's clock is quantized, this implies that the Hartle-Hawking state is not a trace on the resulting crossed-product algebra. We conjecture that the observer's algebra has a trivial commutant. When the time separation between operators exceeds the scrambling time, the OTOC decays to zero and a free product algebra emerges. We illustrate this using classical solutions of de Sitter JT gravity with shocks. We comment on how our results pose a challenge for observer-centric static patch holography.