Revisiting the no-boundary proposal with a scalar field

Jonas, Caroline; Lehners, Jean-Luc; Meyer, Vincent

doi:10.1103/physrevd.105.043529

Cited by 12 publications

(13 citation statements)

References 38 publications

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“…Whereas in the inflationary paradigm, one utilizes the framework of quantum field theory on classical curved backgrounds, in the framework of quantum cosmology, one attempts to deal with a quantum background as well. In this respect, several proposals for the wave function of a de Sitter toy universe were proposed, such as the Hartle-Hawking's or the Vilenkin's proposal, etc., and subsequent works also extended the scenario to include more realistic potentials that drive the inflation [35,36]. However, these proposed semiclassical wave functions do not take into consideration the restriction imposed on the duration of inflation by Swampland conjectures.…”

Section: Discussionmentioning

confidence: 99%

Wave function of the universe in the presence of trans-Planckian censorship

Mondal

2022

Preprint

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The wave function for a closed de Sitter universe has been computed, demanding consistency with the recently proposed Trans-Planckian Censorship Conjecture (TCC). We extend the Einstein-Hilbert action to contain a complex-valued term which provides an exponentially decaying weight for the geometries violating TCC in the Lorentzian path integral sum while working in the minisuperspace approach to quantum cosmology. This postulated modification suppresses the probability of evolution of the universe into configurations that violate TCC. We show that due to the presence of this suppression factor, the Hubble rate of the universe at the end of the inflation gets subdued and assumes a value less than what is expected classically. Moreover, the consequences of this quantum gravity motivated correction in the primordial power spectrum are discussed as well. I. INTRODUCTIONA surprising revelation in the post-nineteenth-century physics was the realization that the laws of quantum physics are more fundamental, of which the classical laws are crude approximations.Given this fundamental characteristic of quantum physics, it begs the question of whether quantum laws, instead of classical ones should govern the evolution of the universe. Even though the present universe might not reveal any quantum behavior, the quantum nature is expected to be critical for its evolution in the early time.Considering the entire universe as a quantum mechanical system is one of the boldest proposals in modern theoretical cosmology. Since the universe is considered as a quantum system, it must be associated with a wave function. The most concrete attempts to compute such a wave function are Hartle-Hawking's "no-boundary proposal" [1] and Vilenkin's "tunneling universe proposal" [2].These proposals consider the scenario of the 'birth' of a de Sitter universe from apparently 'nothing.' However, recent investigations [3,4] into string theory, a well-developed candidate for a theory of quantum gravitation, indicate that effective field theories leading to long-lived de Sitter evolution of the universe belong to the Swampland-a set of low energy effective physics models that are inconsistent with the theory of quantum gravity [5]. The proposed semiclassical wave functions

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Section: Discussionmentioning

confidence: 99%

Wave function of the universe in the presence of trans-Planckian censorship

Mondal

2022

Preprint

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“…it will be of interest to see what happens in scalar field models where the full minisuperspace version can be solved analytically, and where the scalar field is not restricted to small changes only (this is work in progress [28]). Furthermore, for steep negative potentials complex no-boundary instantons with late-time ekpyrotic evolution also exist [29,30].…”

Section: Discussionmentioning

confidence: 99%

“…It will be of interest to extend the current analysis to a scalar field model that can be solved exactly in minisuperspace, and where we are not limited to small excursions of the scalar field. Such a model will be presented in upcoming work [28].…”

Section: Scalar Fieldmentioning

confidence: 99%

The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials

Lehners

2021

Preprint

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We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.

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“…Another argument for why one should only consider real matter fields is that for p-forms with p ≥ 1 (i.e., not scalar fields) the field configurations also include some integer variables often called the monopole numbers, the instanton numbers, or the fluxes, and integers cannot be analytically continued, though, as noted in [8], this would only lead to a weaker global, and not a local, restriction. Finally, we point out that the addition of a complex scalar field in the no-boundary proposal introduces strong non-localities since in that case the South Pole values of the scalar field are found to depend on the final size of the universe [18], leading to the highly non-local picture of a universe constantly 'recalculating itself' as it expands -this effect can be avoided if the scalar field remains real and at an extremum of the potential.…”

Section: The Lsksw Allowability Criterionmentioning

confidence: 99%

Uses of Complex Metrics in Cosmology

Jonas,

Lehners,

Quintin

2022

Preprint

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Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more probable than ordinary classical evolution. In the cosmological context, we investigate a criterion proposed by Witten (based on works of Kontsevich & Segal and of Louko & Sorkin) to decide whether a complex metric is allowable or not. Because of the freedom to deform complex metrics using Cauchy's theorem, deciding whether a metric is allowable in general requires solving a complicated optimisation problem. We describe a method that allows one to quickly determine the allowability of minisuperspace metrics. This enables us to study the off-shell structure of minisuperspace path integrals, which we investigate for various boundary conditions. Classical transitions always reside on the boundary of the domain of allowable metrics, and care must be taken in defining appropriate integration contours for the corresponding gravitational path integral. Perhaps more surprisingly, we find that proposed quantum ('tunnelling') transitions from a contracting to an expanding universe violate the allowability criterion and may thus be unphysical. No-boundary solutions, by contrast, are found to be allowable, and moreover we demonstrate that with an initial momentum condition an integration contour over allowable metrics may be explicitly described in arbitrary spacetime dimensions.

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Revisiting the no-boundary proposal with a scalar field

Cited by 12 publications

References 38 publications

Wave function of the universe in the presence of trans-Planckian censorship

Wave function of the universe in the presence of trans-Planckian censorship

The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials

Uses of Complex Metrics in Cosmology

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