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.

V2: 1+33 pages, 5 figures, text modified at few places, some typos corrected, references added. Accepted for publication in JHEP

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• Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
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• Boundary choices and one-loop complex gravitational path integral
• Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
• Quantum cosmology of the flat universe via closed real-time path integral
• No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology
• Complex Saddles of Charged-AdS Gravitational partition function
• Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW