Bodmann, B.A.L.; Vasconcellos, C.A.Z.; Bechstedt, P.O.H.; de Freitas Pacheco, J.A.; Hadjimichef, D.; Razeira, M.; Degrazia, G.A. A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters. Universe2023, 9, 278.
Bodmann, B.A.L.; Vasconcellos, C.A.Z.; Bechstedt, P.O.H.; de Freitas Pacheco, J.A.; Hadjimichef, D.; Razeira, M.; Degrazia, G.A. A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters. Universe 2023, 9, 278.
Bodmann, B.A.L.; Vasconcellos, C.A.Z.; Bechstedt, P.O.H.; de Freitas Pacheco, J.A.; Hadjimichef, D.; Razeira, M.; Degrazia, G.A. A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters. Universe2023, 9, 278.
Bodmann, B.A.L.; Vasconcellos, C.A.Z.; Bechstedt, P.O.H.; de Freitas Pacheco, J.A.; Hadjimichef, D.; Razeira, M.; Degrazia, G.A. A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters. Universe 2023, 9, 278.
Abstract
In this contribution to the Festschrift for Prof. Remo Ruffini, we investigated a formulation of quantum gravity based on the Wheeler-DeWitt (WDW) equation combined with the classical concepts of the branch-cut cosmology, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction phase, prior to the primordial singularity, and the subsequent expansion phase. 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 cosmology as well as the corresponding conjugate momentum to the category of quantum operators. As a novelty, 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 the integers α=[0,1,2], since non-integers have no physical meaning, allowing this way a broader class of solutions for the wave function of the Universe. As another novelty, additional energy-dependent parametrizations are considered, more specifically, in addition to a branched universe filled with underlying background vacuum energy, matter and radiation, in order to make contact with standard model calculations, we additionally supplement the formulation with baryon matter, dark matter and quintessence contributions. As an additional novelty, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate this way, as a novelty conclusion, 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.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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