Structural Resolution of the Core-Cusp Problem and Dynamics of the Emergent Halo in Environmental Transition Cosmology (ETC)

This research monograph investigates the structural resolution of the galactic core-cusp problem and the dynamics of the emergent halo within the framework of Environmental Transition Cosmology (ETC). By replacing the singular central behavior of standard cold dark matter profiles (such as NFW) with a saturating pseudo-isothermal profile under the central saturation boundary condition lim⁡r→0dρdr=0\lim_{r\to 0}\frac{d\rho}{dr}=0limr→0drdρ=0, the core-cusp tension is resolved analytically. The inner rotation curve naturally exhibits a rigid-body behavior (V(r)∝rV(r) \propto rV(r)∝r with slope γ=1.0\gamma=1.0γ=1.0), in agreement with high-resolution observations of dwarf and low-surface-brightness galaxies (e.g., DDO 154, where γ=0.98±0.08\gamma=0.98\pm0.08γ=0.98±0.08). Furthermore, the universal surface density relation (μ0=ρ0rc≈100–140 M⊙/pc2\mu_0 = \rho_0 r_c \approx 100\text{--}140\ M_\odot/\mathrm{pc}^2μ0=ρ0rc≈100–140 M⊙/pc2,log10μ0≈2.08±0.18) emerges as a natural scaling feature of the model. The manuscript bridges small-scale galactic dynamics with large-scale environmental transition parameters, establishing a unified continuity between early primordial nodes and late-time galactic structures.