Cosmic Inflation in an Extended Noncommutative Foliated Quantum Gravity: The Wave Function of the Universe

We explore a noncommutative extension of branch‐cut quantum gravity (BCQG), with a focus on its implications for early‐universe inflation. Our framework builds on a three‐field mini‐superspace model involving a complex‐valued cosmic‐scale factor, a perfect‐fluid field, and an inflaton‐type scalar field. Using a Faddeev–Jackiw symplectic deformation of the conventional Poisson algebra, we construct a noncommutative phase space and derive a modified Wheeler–DeWitt equation. Analytic solutions to the wave function of the universe are obtained and analyzed. We show that noncommutativity induces coupling between ultraviolet and infrared modes, naturally leading to an inflationary phase without requiring fine‐tuned initial conditions. This feature offers a novel alternative to standard inflationary models. We also discuss how the structure of the wave function in this framework may relate to primordial density perturbations. While some aspects of this theory remain speculative, the mathematical formulation provides a consistent path toward integrating quantum gravitational effects into early cosmological dynamics.