On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization
Abstract
Recently there has been a surge of interest in studying Lorentzian quantum cosmology using Picard-Lefschetz methods. The present paper aims to explore the Lorentzian path-integral of Gauss-Bonnet gravity in four spacetime dimensions with metric as the field variable. We employ mini-superspace approximation and study the variational problem exploring different boundary conditions. It is seen that for mixed boundary conditions non-trivial effects arise from Gauss-Bonnet sector of gravity leading to additional saddle points for lapse in some case. As an application of this we consider the No-boundary proposal of the Universe with two different settings of boundary conditions, and compute the transition amplitude using Picard-Lefschetz formalism. In first case the transition amplitude is a superposition of a Lorentzian and a Euclidean geometrical configuration leading to interference incorporating non-perturbative effects coming from Gauss-Bonnet sector of gravity. In the second case involving complex initial momentum we note that the transition amplitude is an analogue of Hartle-Hawking wave-function with non-perturbative correction coming from Gauss-Bonnet sector of gravity.
Cite
@article{arxiv.2101.04644,
title = {On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization},
author = {Gaurav Narain},
journal= {arXiv preprint arXiv:2101.04644},
year = {2021}
}
Comments
V2: 1+33 pages, 5 figures, text modified at few places, some typos corrected, references added. Accepted for publication in JHEP