Degenerate Dark Matter at Galactic Scales: A BCS Theory

We show that if dark matter in a typical galaxy is a degenerate Fermi gas, particles should have a mass of $\sim$ 1eV for the galaxy to be stable. While this is the mass range of the active neutrinos, they are not a dark matter candidate in SM-GR-$\mathrm{\Lambda }$-CDM. To show that the bounds on active neutrino dark matter are model dependent, we explore the predictions of SM-LGT cosmological model. First, primordial neutrinos are predicted to freeze-out non-relativistically at early universe without affecting the expansion rate. Second, they make a degenerate gas in galaxies at the present time. Third, SM-LGT Hamiltonian at low temperatures is identical with that of the BCS theory of superconductivity. Consequently, there exists a narrow band of compressible condensed bosonic bound states on top of the Fermi surface which forms some denser structures.