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.