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Abstract We study quantum cosmology of the 2DJackiw-Teitelboim (JT) gravity with Λ > 0 and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections ofS1×S2topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate boundary conditions and employing the methods of Picard-Lefschetz theory. The JT-KS connection formulas allow us to translate this result to JT gravity, define the HH wave function and obtain a probability distribution for the dilaton field.
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The tunneling wavefunction in Kantowski-Sachs quantum cosmology
Abstract We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology S 1 × S 2 and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both S 1 and S 2 are set equal to zero, the wave function describes (semiclassically) a universe originating at a singularity. This may be interpreted as indicating that an S 1 × S 2 universe cannot nucleate out of nothing in a non-singular way. Here we explore an alternative suggestion by Halliwell and Louko that creation from nothing corresponds in this model to setting the initial volume to zero. We find that the only acceptable version of this proposal is to fix the radius of S 1 to zero, supplementing this with the condition of smooth closure (absence of a conical singularity). The resulting wave function predicts an inflating universe of high anisotropy, which however becomes locally isotropic at late times. Unlike the de Sitter model, the total nucleation probability is not exponentially suppressed, unless a Gauss-Bonnet term is added to the action.
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- Award ID(s):
- 2110466
- PAR ID:
- 10462647
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2022
- Issue:
- 08
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 069
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1475-7516/2022/08/069
