Inflation in a Non‐Commutative Riemannian‐Foliated Quantum Gravity Domain

ABSTRACT

We explore the implications of Branch‐Cut Quantum Gravity (BCQG), a novel framework leveraging non‐commutative geometry within a symplectic phase‐space, on the accelerated expansion of the universe. Non‐commutativity, introduced through a deformation of the Poisson algebra and enhanced by a symplectic metric, provides a robust mechanism for addressing key challenges in cosmology, such as the youngness paradox and the fine‐tuning of initial conditions in standard inflationary models. By embedding quantum dual‐field dynamics within a Riemannian‐foliated spacetime, BCQG naturally integrates short‐ and long‐range spacetime effects into a unified formalism. This approach offers an alternative to standard inflationary models by predicting cosmic acceleration through geometric restructuring rather than finely‐tuned initial states. In contrast to models like ΛCDM or String Theory, BCQG introduces unique corrections to cosmic scale factors and predicts a novel transition between contraction and expansion phases via topological branch‐cuts, circumventing the singularity problem. Moreover, BCQG's non‐commutative formulation provides testable predictions, such as modifications in cosmic microwave background (CMB) anisotropies and large‐scale structure evolution. We discuss the mathematical foundation, observational implications, and future avenues for validating BCQG through astrophysical data, positioning it as a promising theoretical alternative for understanding the universe's accelerated growth.