Chaos and the Emergence of the Cosmological Horizon

          @misc{ pirsa_PIRSA:25060003,
            doi = {10.48660/25060003},
            url = {https://pirsa.org/25060003},
            author = {Kolchmeyer, David},
            keywords = {Quantum Gravity, Quantum Information},
            language = {en},
            title = {Chaos and the Emergence of the Cosmological Horizon},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060003 see, \url{https://pirsa.org}}
          }
          

Abstract

We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work (CLPW) that their algebras are mutually commuting type II_1 factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute out-of-time-ordered correlators along an observer's worldline, and observe a Lyapunov exponent given by 4πβ_dS, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the chaos bound associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for de Sitter holography.