Preprint

PUBDB-2024-05057

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png DeWitt wave functions for de Sitter JT gravity

Buchmuller, W. (Corresponding author)Extern* ; Hebecker, A. ; Westphal, A.DESY*

2024

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Please use a persistent id in citations: doi:10.3204/PUBDB-2024-05057

Report No.: DESY-24-105; arXiv:2412.09211

Abstract: Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space is an intriguing model for cosmological ``wave functions of the universe'. Its minisuperspace version already contains all physical information. The size of compact slices is parametrized by a scale factor $h > 0$. The dilaton $\phi$ is chosen to have positive values, $\phi > 0$, and interpreted as size of an additional compact slice in a higher-dimensional theory. At the boundaries $h=0$, $\phi=0$, where the volume of the universe vanishes, the curvature is generically singular. According to a conjecture by DeWitt, solutions of the Wheeler-DeWitt (WDW) equation should vanish at singular loci. Recently, the behaviour of JT wave functions at large field values $h$, $\phi$ has been obtained by means of a path integral over Schwarzian degrees of freedom of a boundary curve. We systematically analyze solutions of the WDW equation with Schwarzian asymptotic behaviour. We find real analytic solutions that vanish on the entire boundary, in agreement with DeWitt's conjecture. Projection to expanding and contracting branches may lead to singularities, which can however be avoided by an appropriate superposition of solutions. Our analysis also illustrates the limitations of semiclassical wave functions.

Note: 57 pages, 10 figures

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe (390833306) (390833306)
3. SFB 1624 B03 - Modulräume und Quantengravitation (B03) (531727554) (531727554)
4. DFG project G:(GEPRIS)471314740 - Holographie und das Swampland: Konsistenzbedingungen an fundamentale Physik aus der Quantengravitation (471314740) (471314740)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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