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No Rescue for the No Boundary Proposal: Pointers to the future of quantum cosmology

Feldbrugge, J., Lehners, J.-L., & Turok, N. (2018). No Rescue for the No Boundary Proposal: Pointers to the future of quantum cosmology. Physical Review D, 97: 023509. doi:10.1103/PhysRevD.97.023509.

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### Creators

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Creators:
Feldbrugge, Job, Author
Lehners, Jean-Luc1, Author
Turok, Neil, Author
Affiliations:
1String Cosmology, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1753351

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract: In recent work, we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, {\it i.e}, a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime "from nothing". Furthermore, we found the linearized perturbations to be governed by an {\it inverse} Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro {\it et al.} followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, non-perturbative corrections which again render the perturbations unsuppressed. We prove there is {\it no} choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.

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Dates: 2017-08-162017-12-102018
Publication Status: Published in print
Pages: 60 pages, 13 figures. Version to appear in Phys. Rev. D, including minor amendments and two new figures showing the effects of nonlinear backreaction to be modest
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Rev. Method: -
Identifiers: arXiv: 1708.05104
DOI: 10.1103/PhysRevD.97.023509
URI: http://arxiv.org/abs/1708.05104
Degree: -

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Title: Physical Review D
Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 97 Sequence Number: 023509 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258