Abstract
Recently there has been a surge of interest in studying Lorentzian quant urn 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.
Highlights
Researchers have tried to address this issue in different ways: (1) modify the standard model by incorporating dark-matter and dark-energy while keeping GR to be unmodified, (2) modify gravitational dynamics at large distances keeping the standard model unmodified or (3) modify both GR and standard model
The present paper aims to explore the Lorentzian path-integral of Gauss-Bonnet gravity in four spacetime dimensions with metric as the field variable
Overtime a need arose of having a modification of GR which consist of higherderivatives of the metric field, but when contributions from all such terms are summed over the highest order of time derivative is only two
Summary
The FLRW metric given in eq (1.2) is conformally related to flat metric and its Weyl-tensor Cμνρσ = 0. The non-zero entries of the Riemann tensor are [51,52,53]. Where gij is the spatial part of the FLRW metric and (′) denotes derivative with respect to tp. For the Ricci-tensor the non-zero components are. In the case of Weyl-flat metrics one can express Riemann tensor in terms of Ricci-tensor and Ricci scalar
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