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Chaos and complementarity in de Sitter space
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We consider small perturbations to a static three-dimensional de Sitter geometry. For early enough perturbations that satisfy the null energy condition, the result is a shockwave geometry that leads to a time advance in the trajectory of geodesics crossing it. This brings the opposite poles of de Sitter space into causal contact with each other, much like a traversable wormhole in Anti-de Sitter space. In this background, we compute out-of-time-order correlators (OTOCs) to asses the chaotic nature of the de Sitter horizon and find that it is maximally chaotic: one of the OTOCs we study decays exponentially with a Lyapunov exponent that saturates the chaos bound. We discuss the consequences of our results for de Sitter complementarity and inflation.
Forward citations
Cited by 9 Pith papers
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Anti-scrambling and euclidean folds from observer correlators in de Sitter space
Semiclassical gravity in de Sitter space produces four-point observer correlators whose sign of the scrambling correction is opposite to the black-hole case (anti-scrambling); the authors propose bounded-energy quantu...
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Anti-scrambling and euclidean folds from observer correlators in de Sitter space
Observer correlators in de Sitter exhibit anti-scrambling with a positive OTOC correction and 2π/β Lyapunov exponent, and a Euclidean-folding prescription for bounded-energy quantum systems is proposed.
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A de Sitter Anti-Scrambling Algebra
In a toy model of de Sitter quantum gravity, shockwave time advances break the KMS condition and prevent the Hartle-Hawking state from being a trace on the observer's crossed-product algebra.
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Out-of-time-ordered Correlators in de Sitter Revisited
The de Sitter OTOC grows at the maximal Lyapunov rate 2π/β at tree level and at twice that rate in a massive-graviton-regulated double-scaling limit, with the growth traced to large diffeomorphisms in the graviton propagator.
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Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons
Pole-skipping in Schwarzschild-de Sitter predicts superluminal and imaginary butterfly velocities, confirmed by shock wave analysis, hinting at nonlocal and non-Hermitian dual dynamics.
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Negative shocks versus static patch holography
Out-of-time-order correlators along a de Sitter observer worldline, computed with the shockwave eikonal formalism including recoil and backreaction, violate the cyclicity and positivity required of a trace, falsifying...
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Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
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Towards a microscopic description of de Sitter dynamics
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
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A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification
The claimed RL safety verification framework is absent from the manuscript; the body text is an unrelated high-energy physics paper about de Sitter horizon chaos.
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