Induced Superfluid Cosmology: A Theoretical Framework for Emergent Gravity and Dark Matter

Abstract: Induced Gravity and Harmonic Mass Spectrum in a Superfluid Vacuum We present a theoretical framework for emergent spacetime based on chiral symmetry breaking in a Planck-scale fermion condensate. Using a topological field theory approach on a torus manifold $T^2$, we derive the mass spectrum of elementary particles as resonant breathing modes of vortex loops. This yields a Master Spectral Law: $m(p,q) = M^(1/p + 1/q)$, where $M^ \approx 365$ GeV is the symmetry-breaking scale. This framework offers a unified resolution to several open problems: Hierarchy Problem: The weak scale emerges naturally via a BCS-type dimensional transmutation mechanism ($\Lambda_{UV} \to M^*$). Mode Selection: We prove that the observed particle spectrum (Higgs, W, Z) corresponds to the lowest-complexity topological sectors ($p=5$ and $p=q$), uniquely determined by constrained optimization. Dark Sector: The model predicts a specific "Dark Tower" of high-winding composite solitons ($p=q=2^n$) that function as Self-Interacting Dark Matter (SIDM), consistent with formation structure and Vainshtein screening in the solar system.