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

Abstract

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 $g_i$. 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.