Chaos and complementarity in de Sitter space
arXiv:2002.01326 · doi:10.1007/JHEP05(2020)152
Abstract
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.
arXiv comment30 pages, 7 figures. v2: References and clarifications added. v3: Fixed typo in derivation of the shockwave geometry in appendix A
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