Information-Geometric Formation of Dwarf Galaxies in the Fuzzy Dark Matter Paradigm

We present a unified, information-geometric formulation of structure formation in the fuzzy dark matter (FDM) paradigm, in which the Schrödinger-Poisson dynamics of ultralight bosons defines a geometric flow on the statistical manifold of smooth density fields. Within this framework, the interplay between quantum pressure, gravitational self-interaction, and baryonic response yields stable, self-gravitating cores that naturally trap gas and stars into finite-mass, cored systems. Rigorous existence and stability theorems for coupled baryon-dark matter equilibria demonstrate that solitonic or Thomas-Fermi configurations represent stationary points of an underlying Fisher-type entropy functional, providing a covariant mechanism for halo relaxation and baryon confinement. This approach overcomes key small-scale challenges of both ΛCDM and conventional FDM models, including the core-cusp tension and the inefficient coupling between baryons and dark matter. When applied to Milky-Way satellite galaxies (Fornax, Sculptor, Leo I and Leo II) using Gaia DR3 and DES datasets, the predicted equilibrium profiles produce observed core radii of 0.3-1 kpc and stellar velocity dispersions of 6-11 kms^-1. The results suggest that dwarf galaxies form and evolve along an information-driven curvature flow towards gravitational equilibrium, unifying quantum coherence and macroscopic structure formation in the low-mass regime.