Cosmic Inflation in an Extended Non-Commutative Foliated Quantum Gravity: Friedmann-Type Dynamical Equations

A novel approach to cosmic inflation within the framework of a non-commutative Riemannian foliated quantum gravity, built upon a reverse Faddeev–Jackiw symplectic spacetime deformation of the conventional Poisson algebra, is investigated. Friedmann-type dynamical equations, analitycally continued to a complex non-commutative framework, incorporate a modified energy-momentum Riemann tensor and a non-commutative 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 play a central role, providing a natural topological mechanism for inflation and recursal evidences 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 predict by the Riemann foliated quantum gravity, offering potential connections to observational cosmology.