Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Vieira, H. S.; Bezerra, V. B.; Muniz, C. R.; Cunha, M. S.; Christiansen, H. R.

doi:10.1016/j.physletb.2020.135712

Cited by 14 publications

(15 citation statements)

References 7 publications

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“…The Hořava-Lifshitz action,  HL , is given by (Abreu et al 2019;Bertolami & Zarro 2011;Bodmann et al 2023a;Bodmann et al 2023b;Cordero et al 2019;García-Compeán & Mata-Pacheco 2022;Hess et al 2023;Hořava 2009;Vieira et al 2020):…”

Section: Ho řAva-lifshitz Branch-cut Actionmentioning

confidence: 99%

“…In the BCG formulation, the action  HL depends on the scalar curvature of the branched Universe, , and on its derivatives, in different orders (Abreu et al 2019;Bertolami & Zarro 2011;Bodmann et al 2023a;Bodmann et al 2023b;Cordero et al 2019;García-Compeán & Mata-Pacheco 2022;Hess et al 2023;Hořava 2009;Vieira et al 2020). In expression (3), g i denote running coupling constants, M P is the Planck mass, ∇ i represents covariant derivatives, and the branching Ricci components of the three-dimensional metrics may be determined by imposing a maximum symmetric surface foliation (Hess et al 2023) which gives:…”

Section: Ho řAva-lifshitz Branch-cut Actionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Ho řAva-lifshitz Branch-cut Actionmentioning

confidence: 99%

Section: Ho řAva-lifshitz Branch-cut Actionmentioning

confidence: 99%

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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show abstract

“…Many relevant questions involving the quantum version of branch‐cut cosmology are still open, such as the role of complex potentials, the presence of higher spatial curvature terms in the formulation, the quantization of helix‐type solutions, more in tune with the classical formulation, a more consistent evolution mapping of the cut‐planes, the consequences of adopting a non‐symmetric approach and a different ordering of the dimensionless thermodynamics connection ϵ , the role of dark matter in the evolution of the branch‐cut universe, the role of fluctuations in the primordial spectrum and seeds in the early universe, and also questions regarding the multiverse content, as well as a class of solutions with ordering parameters (see Vieira et al 2020) among others.…”

Section: Final Remarksmentioning

confidence: 99%

The branch‐cut cosmology: A topological canonical quantum‐mechanics approach

et al. 2022

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In this contribution, we sketch a branch‐cut quantum formulation of the Wheeler‐DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Hořava‐Lifshitz formulation of gravity, which employs higher spatial‐derivative terms of the spacetime curvature for renormalization reasons. Following standard procedures, the quantization of the Lagrangian density is achieved by raising the Hamiltonian, the dynamical variable , which represents the the branch‐cut complex scale factor, and the conjugate momentum pln to the category of operators. We arrive at a Schrödinger‐type equation with a non‐linear potential. Solutions are then obtained and discussed for different potential parameterizations. The results reinforce the conception of a quantum leap between the contraction and expansion phases of the branch‐cut universe, in good agreement with the Bekenstein criterion.

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“…In the case of a closed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime with a quintessence scalar field as a matter source, the WDW equation was studied independently by Hartle and Hawking in [10] and Vilenkin in [11]. Since then, similar approaches have been widely applied in the literature for many other cosmological models with a minisuperspace description; see for instance [12][13][14][15][16][17][18][19][20] and references therein. Nonetheless, the canonical quantization proposal founded in the initial works by DeWitt and Wheeler is not the unique approach towards quantum cosmology, other attempts are based in string theory [21][22][23] and in loop quantum gravity [24,25].…”

Section: Introductionmentioning

confidence: 99%

Quantum cosmology in f(Q) theory

Dimakis

Paliathanasis

Christodoulakis

2021

Class. Quantum Grav.

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We investigate quantum cosmology in teleparallel f (T )-gravity. We delve extensively into the minisuperspace description within the context of teleparallelism.The f (T )-theory constitutes a second-order theory of gravity, whose cosmological counterpart is delineated by a degenerate point-like Lagrangian. To formulate the Hamiltonian function encompassing all constraints and degrees of freedom inherent to f (T ) cosmology, we employ the Dirac-Bergmann algorithm. Subsequently, we determine the wave function of the universe and introduce a "probabilistic" interpretation. We perform comparisons to some classical solutions to see to what extent the quantum approach can cure classical singularities.

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Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Cited by 14 publications

References 7 publications

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

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

The branch‐cut cosmology: A topological canonical quantum‐mechanics approach

Quantum cosmology in f(Q) theory

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