Fermionic Universe Hypothesis: Dark Component

This record presents a theoretical study of the dark sector within the Fermionic Universe Hypothesis (FUH), in which a single keV‑scale fermion ψ with four‑fermion interactions forms condensates that account simultaneously for dark matter, dark energy, and compact dark objects. The work derives an effective equation of state for the ψ‑condensate across low‑ and high‑density regimes and demonstrates how these phases reproduce galactic halos and core–halo structures, late‑time cosmic acceleration, and nonsingular fermionic cores that can mimic black holes. The parameter space of the model is constrained using phase‑space bounds from dwarf galaxies, cosmological background probes (CMB+BAO+SNe), and existing lensing, black‑hole shadow, and gravitational‑wave observations, leading to an allowed region in (m_ψ, w_ψ(z), M_crit, c_H/Λ) and to concrete predictions for future surveys. The text is intended as a self‑contained reference for phenomenology of FUH and as a roadmap for tests with upcoming experiments such as DESI, Euclid, EHT‑like VLBI arrays, and the LIGO–Virgo–KAGRA, ET, and LISA gravitational‑wave network.