Noncommutative branch-cut quantum gravity with a self-coupling inflaton scalar field: The wave function of the Universe

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 Horava-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 Horava-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.

Automated summary

This article discusses the implications of a noncommutative formulation of branch-cut quantum gravity, exploring the evolution of the Universe's wave function using a mini-superspace structure that follows the noncommutative Poisson algebra and the Horava-Lifshitz quantum gravity. The study incorporates a scalar inflaton field and investigates various inflationary models, obtaining solutions to the wave equations without the need for numerical approximations. The results suggest that the noncommutative algebraic space captures both low and high spacetime scales, driving the exponential acceleration of the Universe.