The branch-cut quantum gravity with a self-coupling inflation scalar field: The wave function of the Universe |
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| Authors: | Fridolin Weber Peter O Hess Benno Bodmann José de Freitas Pacheco Dimiter Hadjimichef Marcelo Netz-Marzola Geovane Naysinger Moisés Razeira César A Zen Vasconcellos |
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| Institution: | 1. Department of Physics, San Diego State University (SDSU), San Diego, California, USA;2. Universidad Nacional Autónoma de Mexico (UNAM), México City, Mexico;3. Universidade Federal de Santa Maria (UFSM), Santa Maria, Brazil;4. Observatoire de la Côte d'Azur, Nice, France;5. Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil;6. Universidade Federal do Pampa (UNIPAMPA), Caçapava do Sul, Brazil |
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| Abstract: | This paper focuses on the implications of a commutative formulation that integrates branch-cutting cosmology, the Wheeler–DeWitt equation, and Ho?ava–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 Ho?ava–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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| Keywords: | branch cut cosmology scalar field inflation |
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