The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

Pinto-Neto, Nelson; Santini, E. Sergio

doi:10.1023/a:1015592724845

Cited by 22 publications

(18 citation statements)

References 21 publications

(22 reference statements)

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“…Among the fundamental questions that come from the quantization of the universe as a whole, one of the most important concerns the interpretation of the wave function of the Universe. In order to extract predictions from it, the Bohm-de Broglie (BdB) ontological interpretation of quantum mechanics [6,7] has been proposed [8,9,10], since it avoids many conceptual difficulties that follow from the application of the standard Copenhagen interpretation to a unique system that contains everything. In opposition to the latter one, the ontological interpretation does not need a classical domain outside the quantized system to generate the physical facts out of potentialities (the facts are there ab initio because the positions and trajectories of the particles (called bohmian trajectories) are considered to be part of objective reality, and hence it can be applied to the Universe as a whole.…”

Section: Introductionmentioning

confidence: 99%

Inflationary nonsingular quantum cosmological model

Falciano¹,

Pinto-Neto²,

Santini

2007

Phys. Rev. D

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A stiff matter-dominated universe modeled by a free massless scalar field minimally coupled to gravity in a Friedmann-Lemaître-Robertson-Walker (FLRW) geometry is quantized. Generalized complex-width gaussian superpositions of the solutions of the Wheeler-DeWitt equation are constructed and the Bohm-de Broglie interpretation of quantum cosmology is applied. A planar dynamical system is found in which a diversity of quantum bohmian trajectories are obtained and discussed. One class of solutions represents non-singular inflationary models starting at infinity past from flat space-time with Planckian size spacelike hypersurfaces, which inflates without inflaton but due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase.

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Section: Introductionmentioning

confidence: 99%

Inflationary nonsingular quantum cosmological model

Falciano¹,

Pinto-Neto²,

Santini

2007

Phys. Rev. D

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“…[17,18,19,20], although the theory remains consistent (Refs. [18,19]), and its geometrical properties depends on the choice of the lapse function. However, in the case of homogeneous spacelike hypersurfaces, a preferred foliation of spacetime is selected, the one where the time direction is perpendicular to the Killing vectors of these hypersurfaces.…”

Section: Simplification Of the Second Order Hamiltonian And Canomentioning

confidence: 85%

Scalar Perturbations in Scalar Field Quantum Cosmology

Falciano

Pinto-Neto

2012

The Twelfth Marcel Grossmann Meeting

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In this paper it is shown how to obtain the simplest equations for the Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the case of scalar fields without potential term. This was done through the implementation of canonical transformations at the classical level, and unitary transformations at the quantum level, without ever using any classical background equation, and it completes the simplification initiated in investigations by Langlois [2], and Pinho and Pinto-Neto [4] for this case. These equations were then used to calculate the spectrum index ns of quantum scalar perturbations of a non-singular inflationary quantum background model, which starts at infinity past from flat space-time with Planckian size spacelike hypersurfaces, and inflates due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase. The result is ns = 3, incompatible with observations.

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“…For the usual formulation of Bohmian dynamics for the full Wheeler-DeWitt theory of quantum gravity, a particular spacelike foliation of space-time or, equivalently, a particular choice of "initial" space-like hypersurface and lapse function, needs to be introduced. Different foliations (or lapse functions) yield different Bohmian theories [9][10][11][12]. So, in this case, the dynamics is not invariant under space-time diffeomorphisms.…”

Section: Wheeler-dewitt Quantization and Bohmian Mechanicsmentioning

confidence: 99%

Wheeler-DeWitt quantization and singularities

2015

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We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaître-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We find that for generic wave functions (i.e., nonclassical wave functions), there is a non-zero probability for a trajectory to be non-singular. This should be contrasted to the consistent histories approach for which it was recently shown by Craig and Singh that there is always a singularity. This result illustrates that the question of singularities depends much on which version of quantum theory one adopts. This was already pointed out by Pinto-Neto et al., albeit with a different Bohmian approach. Our current Bohmian approach agrees with the consistent histories approach by Craig and Singh for single-time histories, unlike the one studied earlier by Pinto-Neto et al. Although the trajectories are usually different in the two Bohmian approach, their qualitative behavior is the same for generic wave functions.

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The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

Cited by 22 publications

References 21 publications

Inflationary nonsingular quantum cosmological model

Inflationary nonsingular quantum cosmological model

Scalar Perturbations in Scalar Field Quantum Cosmology

Wheeler-DeWitt quantization and singularities

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