Noncommutative branch-cut quantum gravity with a self-coupling inflation scalar field: Dynamical equations

This article focuses on a recently developed formulation based on the noncommutative branch-cut cosmology, the Wheeler-DeWitt (WdW) equation, the Hořava–Lifshitz quantum gravity, chaotic and the coupling of the corresponding Lagrangian approach with the inflaton scalar field. Assuming a mini-superspace of variables obeying the noncommutative Poisson algebra, we examine the impact of the inflaton scalar field on the evolutionary dynamics of the branch-cut Universe scale factor, characterized by the dimensionless helix-like function ${\ln }^{-1}\left[\beta \left(t\right)\right]$. This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the primordial singularities. We take the Hořava–Lifshitz action modeled by branch-cut quantum gravity as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives and which preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We then investigate the sensitivity of the scale factor of the branch-cut Universe's dynamics.