Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime

Understand

We discuss JT gravity in AdS and dS space in the second order formalism.

• For the pure dS JT theory without matter, we show that the path integral gives rise in general to the Hartle-Hawking wave function which describes an arbitrary number of disconnected universes produced by tunnelling "from nothing", or to transition amplitudes which describe the tunnelling of an initial state consisting of several contracting universes to a final state of several expanding universes.
• These processes can be described by a hologram consisting of Random Matrix Theory (RMT) or, we suggest, after some modification on the gravity side, by a hologram with the RMT being replaced by SYK theory.
• In the presence of matter, we discuss the double trumpet path integral and argue that with suitable twisted boundary conditions, a divergence in the moduli space integral can be avoided and the system can tunnel from a contracting phase to an expanding one avoiding a potential big bang/big crunch singularity.