Chaos and complementarity in de Sitter space

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.

Shocks and Information Exchange in de Sitter Space

“…South Pole As for the eternal black hole in AdS we can derive a simple bound on the information that can be sent through the wormhole, generalizing the result in [19], employing the bounds on the energy of de Sitter shockwaves that we introduced. First we remind the reader that in three dimensions the maximal shift α on a (null) geodesic crossing the shockwave is of the order of the Hubble length, when 2N s = S dS , where N s corresponds to the energy in units of the de Sitter temperature.…”

“…Primary among those is the fact that there exists a maximum energy state in de Sitter space and correspondingly a highest (isotropic and positive) energy shockwave. Having outlined the general idea let us now introduce a few more details, starting with some results of [19].…”

“…Here we will restrict ourselves to the three-dimensional case, where the relevant geometry corresponds to a particle with mass m, bounded by m < 1 8G N , at the center of the static patch. The final result for a shockwave in global lightcone coordinates travelling along the v = 0 horizon is [19]…”

“…Following up on recent work by two of us [19], we propose a bulk procedure that allows the exchange of information between antipodal de Sitter observers after a scrambling time t = H −1 log(S dS ). This is consistent with de Sitter complementarity and the results of Hayden and Preskill [20].…”

Constraints on the duration of inflation from entanglement entropy bounds

“…where H denotes the Hubble parameter during inflation. Although the physical motivation behind this conjecture -a trans-Planckian mode should never become part of late-time macroscopic inhomogeneities -has been heavily debated [4,5], it does find some connections to other aspects of the ST 'swampland' [6][7][8][9][10][11]. In particular, a corollary of this is that only extremely short-lived de Sitter (dS) spaces can arise in a UV-consistent theory [2,3].…”