Minisuperspace quantum cosmology from the Einstein-Cartan path integral
File(s)
Published version
Author(s)
Isichei, Raymond
Magueijo, João
Type
Journal Article
Abstract
We derive the fixed-
Λ
and unimodular propagators using the path integral formalism as applied to the Einstein-Cartan action. The simplicity of the action (which is linear in the lapse function) allows for an exact integration starting from the lapse function and the enforcement of the Hamiltonian constraint, leading to a product of Chern-Simons states if the connection is fixed at the endpoints. No saddle point approximation is needed. Should the metric be fixed at the endpoints, then, depending on the contour chosen for the connection, Hartle-Hawking or Vilenkin propagators are obtained. Thus, in this approach one trades a choice of contour in the lapse function for one in the connection, where appropriate. The unimodular propagators are also trivial to obtain via the path integral, and the previously derived expressions are recovered.
Λ
and unimodular propagators using the path integral formalism as applied to the Einstein-Cartan action. The simplicity of the action (which is linear in the lapse function) allows for an exact integration starting from the lapse function and the enforcement of the Hamiltonian constraint, leading to a product of Chern-Simons states if the connection is fixed at the endpoints. No saddle point approximation is needed. Should the metric be fixed at the endpoints, then, depending on the contour chosen for the connection, Hartle-Hawking or Vilenkin propagators are obtained. Thus, in this approach one trades a choice of contour in the lapse function for one in the connection, where appropriate. The unimodular propagators are also trivial to obtain via the path integral, and the previously derived expressions are recovered.
Date Issued
2023-01-26
Date Acceptance
2023-01-13
Citation
Physical Review D, 2023, 107 (2), pp.1-8
ISSN
2470-0010
Publisher
American Physical Society (APS)
Start Page
1
End Page
8
Journal / Book Title
Physical Review D
Volume
107
Issue
2
Copyright Statement
© 2023 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
License URL
Identifier
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.107.023526
Article Number
023526
Date Publish Online
2023-01-26