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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 7 Pith papers
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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
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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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A family of SU(2) and SU(3) Lipkin-Meshkov-Glick-type Hamiltonians reproduces de Sitter quasinormal-mode densities of states, and late-time probes reveal integrability beneath saddle-dominated scrambling.
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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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