Real no-boundary wave function in Lorentzian quantum cosmology

Dorronsoro, Juan Diaz; Halliwell, J. J.; Hartle, James B.; Hertog, Thomas; Janssen, Oliver

doi:10.1103/physrevd.96.043505

Cited by 101 publications

(131 citation statements)

References 37 publications

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“…Our discussion represents an extension of recent studies of the no-boundary proposal [11], based on the Lorentzian path integral for gravity. In those works, we found an interesting interplay between the cosmological background and the perturbations [12][13][14][15][16][17], see also [18].…”

Section: Introductionmentioning

confidence: 84%

Quantum incompleteness of inflation

et al. 2019

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Inflation is most often described using quantum field theory (QFT) on a fixed, curved spacetime background. Such a description is valid only if the spatial volume of the region considered is so large that its size and shape moduli behave classically. However, if we trace an inflating universe back to early times, the volume of any comoving region of interest -for example the present Hubble volume -becomes exponentially small. Hence, quantum fluctuations in the trajectory of the background cannot be neglected at early times. In this paper, we develop a path integral description of a flat, inflating patch (approximated as de Sitter spacetime), treating both the background scale factor and the gravitational wave perturbations quantum mechanically.We find this description fails at small values of the initial scale factor, because two background saddle point solutions contribute to the path integral. This leads to a breakdown of QFT in curved spacetime, causing the fluctuations to be unstable and out of control. We show the problem may be alleviated by a careful choice of quantum initial conditions, for the background and the fluctuations, provided that the volume of the initial, inflating patch is larger than H −1 in Planck units with H the Hubble constant at the start of inflation. The price of the remedy is high: not only the inflating background, but also the stable, Bunch-Davies fluctuations must be input by hand. Our discussion emphasizes that, even if the inflationary scale is far below the Planck mass, new physics is required to explain the initial quantum state of the universe.

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Section: Introductionmentioning

confidence: 84%

Quantum incompleteness of inflation

et al. 2019

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“…Prior works have studied various potential definitions mainly by exploring different contours of integration for the lapse integral, see e.g. [3,[5][6][7]. Here we will try an alternative route, which is to explore different possibilities for the boundary conditions [3,8,9].…”

Section: Introductionmentioning

confidence: 99%

No-boundary prescriptions in Lorentzian quantum cosmology

2019

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We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

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“…The theory of quantum gravity is as yet unavailable, thus our discussion merely aims to shed some light on the possible behaviour of the classical saddle point solutions that hopefully would dominate the full quantum path integral. Having said that, it must be noted though, that whether such a semi-classical approach even makes sense in the gravitational context is presently subject to debate [67,68]. Furthermore, one could also note that the criteria for the onset of quantum gravity, based on dimensional analysis, is not Lorentz invariant unless one demands macroscopically separated events connected by null rays also be treated quantum gravitationally [69], a prospect that has not been shown to be necessary.…”

Section: Discussionmentioning

confidence: 99%

Alternative route towards the change of metric signature

Zhang

2019

Phys. Rev. D

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Beginning with Hartle and Hawking's no-boundary proposal, it has long been known that the pathology of a big bang singularity can be suppressed if a transition into Riemannian (Euclidean) metric signature (the usual singularity theorems become invalid in this region) occurs when we track back along cosmic time. A vital component of this type of models, that needs to be clarified, is the set of junction conditions at the boundary between the two signature regimes. In the traditional approach, the signature change occurs in the temporal sector through a switch of sign in the lapsesquared function. Motivated by more straightforward connections with the big bang cosmology, we explore here an alternative whereby the spatial metric eigenvalues change sign instead, so that the Riemannian side is purely timelike. We investigate the junction conditions required in this case. PACS numbers: 95.30.Sf, 98.80.Jk, 04.20.-q arXiv:1909.10669v1 [gr-qc]

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Real no-boundary wave function in Lorentzian quantum cosmology

Cited by 101 publications

References 37 publications

Quantum incompleteness of inflation

Quantum incompleteness of inflation

No-boundary prescriptions in Lorentzian quantum cosmology

Alternative route towards the change of metric signature

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