Novel Solution of Wheeler-DeWitt Theory

Glinka, Łukasz Andrzej

doi:10.12691/amp-2-3-3

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…The canonical quantization Dirac procedure applied to the Einstein-Hilbert action results in a second-order functional differential equation defined in general terms in a configuration superspace, whose solutions depend on a three-dimensional metric and on matter fields [37][38][39][40]. Among the different quantization methods, the canonical quantization procedure allows the preservation of the original formal structure of a classical theory, as well as its symmetries and corresponding underlying conservation laws.…”

Section: Discussionmentioning

confidence: 99%

“…The solutions of the WdW equation, represented in turn by a geometric functional of compact manifolds and matter fields, describe the evolution of the quantum wave function of the Universe [38,39]. The most intriguing aspect of the WdW equation, the absence of the time variable, although linked to a classical image of space-time [35], represents a feature of the classical Hamilton-Jacobi formulation of General Relativity, in which the observable universe does not exhibit time-reversal symmetry, giving way to a quantum description of events, as the basic cosmic constituents [40][41][42][43][44]. The wave function, in turn, depends only on a "3-geometry", which corresponds to the equivalence class of metrics under a diffeomorphism.…”

Section: Commutative Quantum Bcg Approachmentioning

confidence: 99%

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A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

Bodmann,

Hadjimichef,

Hess

et al. 2023

Universe

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In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.

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Section: Discussionmentioning

confidence: 99%

Section: Commutative Quantum Bcg Approachmentioning

confidence: 99%

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

Bodmann,

Hadjimichef,

Hess

et al. 2023

Universe

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“…As stressed before, this model, based on the Arnowitt-Deser-Misner decomposition of canonical general relativity in 3 + 1 dimensions, is additionally complemented by a boundary term proposed by the authors of Refs. [37][38][39][40]. Dirac's canonical quantization procedure applied to the Einstein-Hilbert action results in a second-order functional differential equation defined in a configuration superspace, whose solutions depend in general on a three-dimensional induced metric and matter fields [21,25,26,40].…”

Section: Extended Class Of the Branched Quantum Cosmological Solutionsmentioning

confidence: 99%

“…[37][38][39][40]. Dirac's canonical quantization procedure applied to the Einstein-Hilbert action results in a second-order functional differential equation defined in a configuration superspace, whose solutions depend in general on a three-dimensional induced metric and matter fields [21,25,26,40].…”

Section: Extended Class Of the Branched Quantum Cosmological Solutionsmentioning

confidence: 99%

A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters

et al. 2023

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In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

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The branch‐cut quantum gravity with a self‐coupling inflation scalar field: The wave function of the Universe

Weber,

Hess,

Bodmann

et al. 2023

Astron Nachr

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This paper focuses on the implications of a commutative formulation that integrates branch‐cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Building on a mini‐superspace structure, we explore the impact of an inflaton‐type scalar field on the wave function of the Universe. Specifically analyzing the dynamical solutions of branch‐cut gravity within a mini‐superspace framework, we emphasize the scalar field's influence on the evolution of the evolution of the wave function of the Universe. Our research unveils a helix‐like function that characterizes a topologically foliated spacetime structure. The starting point is the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as . The corresponding wave equations are derived and are resolved. The commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. Additionally, we delve into a mini‐superspace of variables, incorporating scalar‐inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions for the wave equations without recurring to numerical approximations.

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Novel Solution of Wheeler-DeWitt Theory

Cited by 3 publications

References 26 publications

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters

The branch‐cut quantum gravity with a self‐coupling inflation scalar field: The wave function of the Universe

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