Two dimensional Nearly de Sitter gravity

TL;DR

This work analyzes nearly $dS_2$ gravity, the JT gravity with positive curvature, focusing on a boundary reparametrization mode that controls quantum corrections in a topologically rich theory that lacks propagating gravitons. The authors compute no-boundary wavefunctions to all orders, reveal a Schwarzian-driven boundary dynamics, and reinterpret sums over topologies via a random-matrix framework akin to Saad–Shenker–Stanford. They then bridge to four-dimensional gravity by showing that near-extremal Schwarzschild–de Sitter geometries admit a long-lived $dS_2\times S^2$ throat whose dynamics reproduce the 2D results, and they relate four-dimensional cosmological correlators to their two-dimensional counterparts in this regime. The paper further develops matter correlators in $dS_2$ and gravity-induced corrections at tree and loop levels, demonstrating how boundary gravitons damp long-distance correlations and offering a tractable setting to study quantum gravitational effects in de Sitter-like spacetimes, with connections to SYK and possible dS/CFT interpretations.

Abstract

We study some aspects of the de Sitter version of Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, we have a boundary mode when we compute observables with a fixed dilaton and metric at the boundary. We compute the no-boundary wavefunctions and probability measures to all orders in perturbation theory. We also discuss contributions from different topologies, borrowing recent results by Saad, Shenker and Stanford. We discuss how the boundary mode leads to gravitational corrections to cosmological observables when we add matter. Finally, starting from a four dimensional gravity theory with a positive cosmological constant, we consider a nearly extremal black hole and argue that some observables are dominated by the two dimensional nearly de Sitter gravity dynamics.

Figures (15)

• Figure 1: The Carter-Penrose diagram of $dS_2$ is a horizontal strip. On top of this diagram we display the regions where $\phi$ goes to $+\infty$ in blue and to $-\infty$ in red, the latter representing some kind of "singularity". In (a) we display (\ref{['Poincare']}) in (b) (\ref{['Global']}) in (c) we see (\ref{['Milne']}). The region covered by the Milne type coordinates is yellow and the region covered by the static coordinates in green. In addition we have a region that corresponds to the interior of a black hole shaded in grey.
• Figure 2: Different configurations of $dS_2$ related by an asymptotic symmetry.
• Figure 3: In (a) we see the integration contour in the complex $\tau$ plane, where $\tau$ is the time coordinate in (\ref{['Global']}). The contour starts at $\tau = i \pi/2$. The usual choice is to run it down along $\tau = i \theta$, for real $\theta$, to $\tau =0$ and then continue along the real and positive $\tau$ axis. (b) Picture for the geometry along the traditional contour. First we get a half sphere and then it is joined to half of global de-Sitter. An alternative choice of contour is displayed by the red dashed line where $\tau = i { \pi \over 2} + \tilde{\tau}$ for real $\tau$. (c) For real $\tilde{\tau}$ the metric is minus the metric in hyperbolic space.
• Figure 4: (a) The superspace for the JT gravity theory after a partial gauge fixing is just the Minkowski space parametrized by $u$ and $v$. The late time region corresponds to $T\gg 1$. Classical solutions correspond to the usual straight lines for classical particles in Minkowski space. The condition that space shrinks smoothly corresponds to a boundary condition at $v =0$ which sets the momentum to be such that all classical trajectories go through the point $u=0$, $v= (2\pi)^2$. The region $u< 0$ corresponds to imaginary $\phi$ and arises after euclidean continuation of the solution. We display two possible classical trajectories. (b) We show the same space for the Euclidean AdS JT gravity theory analyzed in appendix \ref{['AdSPartition']}. The asymptotic region corresponds now to the left Rindler wedge. We also display the trajectories of the classical solutions.
• Figure 5: Sketch of the sum over "negative" trumpet geometries \ref{['CoshGeo']}SSS. To the left we have $-AdS$ as in figure \ref{['HHContour']}(c) and we add contributions with different topologies, also integrated over the size $b$ of the throat.