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

Abstract

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. The resulting spectrum of quantum perturbations which are produced can exhibit interesting departures from scale invariance. We also show that the divergence in moduli space can be avoided for suitable correlators which involve different boundaries in the AdS/dS cases, and suggest that a hologram consisting of the SYK theory with additional matter could get rid of these divergences in general. Finally, we analyse the AdS double trumpet geometry and show that going to the micro-canonical ensemble instead of the canonical one, for the spectral form factor, does not get rid of the divergence in moduli space.

Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity

“…Coordinate systems. Here we summarize various useful coordinates to describe twodimensional de Sitter space (see also [46,61,105]).…”

“…To find the Nariai geometry in d dimensions we follow [6,89] (see also [61,105,106]). First note that using (B.2) the function f (r) factorizes as…”

Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands

“…The regions in Schwarzschild de Sitter parameter space we have explored are very far from the Nariai (extremal) limit where a dS 2 throat emerges: see e.g. [104,105,106,107] for some recent investigations on the latter. Our island solution (38) emerges as a self-consistent solution near the black hole horizon in the regime of very low de Sitter temperature: it would seem that the extremization equation (34) has other solutions as well, pertaining to other regimes of more cosmological relevance, worth exploring.…”

Aspects of AdS2 quantum gravity and the Karch-Randall braneworld

“…Here we notice that we have set the bulk curvature scale l AdS to 1 and the δφ(x) expansion is really the expansion with respect to the dimensionless parameter δφ(x) l AdS14 We refer interested readers to[43][44][45][46][47][48][49][50][51][52]63] for other speculations and investigations of the relationship between JT gravity and AdS3 Einstein's gravity and see[53][54][55][56][57][58][59][60][61][62] for the emergence of JT gravity in other context.…”