Institution: | 1. Universidad Nacional Autónoma de Mexico (UNAM), México City, Mexico;2. Department of Physics, San Diego State University (SDSU), San Diego, California, USA
Department of Physics, University of California at San Diego (UCSD), La Jolla, California, USA;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;7. Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil
International Center for Relativistic Astrophysics Network (ICRANet), Pescara, Italy |
Abstract: | This article focuses on the implications of a noncommutative formulation of branch-cut quantum gravity. Based on a mini-superspace structure that obeys the noncommutative Poisson algebra, combined with the Wheeler–DeWitt equation and Ho?ava–Lifshitz quantum gravity, we explore the impact of a scalar field of the inflaton-type in the evolution of the Universe's wave function. Taking as a starting point the Ho?ava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, the corresponding wave equations are derived and solved. The noncommutative quantum gravity approach adopted preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner Formalism. In this work we delve deeper into a mini-superspace of noncommutative variables, incorporating scalar inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions to the wave equations without resorting to numerical approximations. The results indicate that the noncommutative algebraic space captures low and high spacetime scales, driving the exponential acceleration of the Universe. |