On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization

TL;DR

This paper investigates Lorentzian quantum cosmology with Gauss-Bonnet gravity using Picard-Lefschetz methods, revealing new saddle points and non-perturbative effects in boundary conditions and the universe's wave-function.

Contribution

It introduces the analysis of Gauss-Bonnet gravity in Lorentzian path-integral quantization with boundary conditions, highlighting new saddle points and non-perturbative effects.

Findings

Gauss-Bonnet sector affects saddle points under mixed boundary conditions

Transition amplitude includes interference between Lorentzian and Euclidean geometries

Non-perturbative corrections modify the Hartle-Hawking wave-function

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.