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Z-boson exchange interaction induces attractive force between left-handedneutrino and neutron. The Ginzburg-Landau mean field calculation and theBogoliubov transformation suggest that this attractive force leads toneutrino-neutron pair condensate and super-fluidity. When the result ofsuper-fluid formation is applied to the early universe, horizon scale paircondensate may become a component of dark energy. A further accretion of otherfermions from thermal cosmic medium gives a seed of primordial neutron starsmade of proton, neutron, electron, and neutrino in beta-equilibrium. Primordialneutron stars may provide a mechanism of giving a part or the whole of the darkmatter in the present universe, if a properly chosen small fraction of cosmicthermal particles condenses to neutrino-neutron super-fluid and primordialneutron star not to over-close the universe. The proposal can be verified inprinciple by measuring neutrino burst at primordial neutron star formation andby detecting super-fluid relic neutrinos in atomic experiments at laboratories.

Primordial neutron star; a new candidate of dark matter