Two dimensional Nearly de Sitter gravity (1904.01911v3)

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.

Overview of Two Dimensional Nearly de Sitter Gravity

The paper explores aspects of Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space (dS$_2$). It explores the implications of coupling matter and gravity within this framework, evaluates the gravitational corrections to matter correlators, and connects the findings with higher-dimensional settings, particularly four-dimensional gravity theories with positive cosmological constants. The analysis circumvents propagating degrees of freedom by focusing on boundary modes to compute observables and explores contributions from various topologies.

Classical Wavefunction and Quantum Corrections

The classical wavefunction of the universe is computed under the Hartle-Hawking no-boundary proposal, starting from known solutions in global dS$_2$ space. The wavefunction is expressed as a function of the proper length of a spatial slice with a constant dilaton value, considering both growing modes and oscillatory phases due to the expanding cosmological background. Quantum corrections are incorporated using the dynamics of boundary reparametrization modes via the Schwarzian action, analogous to methods employed in AdS$_2$ contexts.

Sum Over Topologies

The paper extends computations to include sums over topologies, inspired by recent results on JT gravity in AdS$_2$. It leverages the analytic continuation of both space and action to encapsulate contributions from configurations that can be reinterpreted from the AdS context into the de Sitter setting. This leads to the novel suggestion that geometries characterizing the JT gravity in JT-AdS$_2$ sum over all topologies mirror those in JT-dS$_2$, albeit with differing observable implications due to the sign change characteristic of Lorentzian dS background.

Relation to Four Dimensional Gravity and Matter Correlators

Moving beyond two dimensions, the JT theory is connected to nearly extremal black hole solutions in four-dimensional de Sitter space, finding possible interpretations of the universe's wavefunction as systems of coupled oscillators or random matrices. The paper evaluates correlations in nearly dS$_2$, revealing that gravitational effects influence long-distance correlators. Analytical techniques employed showcase reduced two-dimensional calculations that maintain relevance in broader cosmological models.

Technical Contributions and Computational Framework

The paper's robust technical contribution lies in elucidating the Schwarzian dynamics, examining gravitational modes in two dimensions that, while classically vanishing, are pertinent in quantum corrected scenarios. Such reconstructions of dS$_2$ properties offer insights into matter dynamics and gravitational interactions within cosmological models, where direct computation may be infeasible due to scale and complexity. This groundwork allows for consistent speculation on the future development of these theories, potentially extending into realms of quantum gravity and cosmological histories.

In conclusion, the paper analyzes how JT gravity's dS$_2$ character fundamentally alters familiar results, provides a pathway to address cosmological boundary conditions, and speculates in alignment with known theoretical frameworks, like dS/CFT correspondence and holography, while adjusting for the shifted focus from anti-de Sitter space properties. Future research could potentially explore deeper interconnections between JT gravity configurations and higher-dimensional cosmological models, or those within disparate gravitational potential landscapes.