https://doi.org/10.1140/epjc/s10052-021-09315-1
Regular Article - Theoretical Physics
Quantum theory of 
-FLRW-metrics its connection to Chern-Simons-models and the theta vacuum structure of quantum gravity
University of Leipzig, Leipzig, Germany
Received:
14
April
2021
Accepted:
3
June
2021
Published online:
6
July
2021
We show how a foliated 4-dimensional FLRW-metric becomes a gravitational instanton, if the spatial metric minimizes a three-dimensional Einstein–Hilbert action with positive cosmological constant, which is equal to the demand, that the scale factor satisfies the Bogomolny-equation, where the curvature parameter varies over the one-parameter family of hyperslices and takes the role of a potential depending on the scale factor. Additionally, we draw the connection to SO(4)-Chern–Simons theory and show how the established interpolating solutions describe the gradient flow between the minima of the vacuums of the Einstein–Hilbert action, as well as how they can be used to calculate tunnelling-amplitudes of gravitons and trivialize the calculations of path integrals in quantum gravity. All the calculations are carried out particularly for k admitting a 
-symmetry.
The original online version of this article was revised: On the second page on the right-hand side, the following equation was incorrectly typeset: 
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-021-09461-6.
Copyright comment corrected publication 2021
© The Author(s) 2021. corrected publication 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
