Closed universes in two dimensional gravity

TL;DR

<3-5 sentences>In this work, we study closed universes in two-dimensional gravity, focusing on Jackiw-Teitelboim (JT) gravity coupled to matter and a simple topological model to access non-perturbative effects. Perturbatively, JT+matter yields a rich set of semiclassical closed-universe states obtained from trumpet saddles and boundary insertions, with wavefunctionals exhibiting oscillatory and classically allowed regions. Non-perturbatively, spacetime wormholes collapse the closed-universe Hilbert space to a single state per $\alpha$-sector, with the norm $\tr M$ described as a product of a two-sided-wormhole factor and the squared matter one-point function, reflecting an ensemble average over theories. The results illuminate tensions between semi-classical richness and a unique non-perturbative cosmological state, and they connect to broader themes in black-hole interiors, tensor networks, and ensemble averaging in quantum gravity.

Abstract

We study closed universes in simple models of two dimensional gravity, such as Jackiw-Teiteilboim (JT) gravity coupled to matter, and a toy topological model that captures the key features of the former. We find there is a stark contrast, as well as some connections, between the perturbative and non-perturbative aspects of the theory. We find rich semi-classical physics. However, when non-perturbative effects are included there is a unique closed universe state in each theory. We discuss possible meanings and interpretations of this observation.

Figures (13)

• Figure 1: Preparing a closed universe state with a particle (dashed blue).
• Figure 2: Classical solution for a closed universe. It begins at a big bang and re-collapses in a big crunch. The green geodesic is the maximal slice of the universe.
• Figure 3: Matter stabilized Euclidean wormhole (left), and the analytic continuation (right) to real time. The wormhole geometry becomes a closed universe with a heavy massive particle (dashed blue), with a maximal geodesic slice (green circle).
• Figure 4: Boundary conditions preparing a black hole state and a closed universe state
• Figure 5: The grey lines are lines of constant dilaton. (a) shows the double trumpet solution embedded into the hyperbolic disk, with the blue line the massive particle. The green line is the geodesic throat $b_0$. The two blue lines are geodesics and are identified. (b) shows the analytic continuation of the double trumpet into Lorentzian time $\rho \to i t$, where it becomes a closed universe. (c) shows the closed universe solution embedded into a WDW patch.