Anti-scrambling and euclidean folds from observer correlators in de Sitter space

The de Sitter horizon behaves in a qualitatively different way from a black hole horizon, which poses a challenge to any attempt to develop a fundamental quantum description of de Sitter space. In this paper we gather some ``data'' on this problem using gravitational calculations, seeing that they lead to an ``anti-scrambling'' phenomenon that is contrary to the behavior of standard many-body quantum systems. We organize our discussion in terms of correlation functions computed on the worldline of an observer living in the spacetime, with the two-point function looking like a conventional thermal correlator but the four-point function showing anti-scrambling. We propose that anti-scrambling can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.