A Closed and Microscopically Motivated Formulation of Knots Field Cosmology

This paper presents a closed and internally consistent formulation of Knots Field Cosmology, unifying and completing the phenomenological and effective-field approaches introduced in earlier works. The cosmic vacuum is hypothesized to possess non-trivial topological structure, whose coarse-grained complexity is captured by an emergent scalar order parameter, the knots field. A microscopically motivated definition of the field is provided, along with a non-arbitrary effective potential consistent with topological sector periodicity. The framework reproduces late-time cosmic acceleration, flat galactic rotation curves, gravitational lensing behavior, early supermassive black hole formation, and the baryonic Tully–Fisher relation within a single minimally coupled scalar-field theory. Stability, early-universe consistency, and observational falsifiability are explicitly addressed. The model constitutes a single, testable hypothesis suitable for confrontation with cosmological and galactic data.