Cosmic Inflation in an Extended Noncommutative Foliated Quantum Gravity: Friedmann‐Type Dynamical Equations

ABSTRACT A novel approach to cosmic inflation within the framework of a noncommutative Riemannian foliated quantum gravity, built upon a reverse Faddeev–Jackiw symplectic spacetime deformation of the conventional Poisson algebra, is investigated. Friedmann‐type dynamical equations, analytically continued to a complex noncommutative framework, incorporate a modified energy‐momentum Riemann tensor and a noncommutative matter‐energy potential, highlighting the emergence of quantum gravity topological fluctuation effects on the expansion dynamics of the universe. In this realm, the coupling of UV and IR scales plays a central role, providing a natural topological mechanism for inflation and recursal evidence for the generation of relic gravitational waves. These predictions align with a self‐consistent description of the transition between the primordial mirror‐universe deceleration and present‐universe acceleration phases as predicted by the Riemann foliated quantum gravity, offering potential connections to observational cosmology.