 Solution

A large neutrino degeneracy parameter raises the relativistic energy density and therefore the expansion rate. Big Bang nucleosynthesis tests this through primordial light-element abundances; an electron-neutrino chemical potential also shifts neutron--proton chemical equilibrium directly. The Cosmic microwave background power spectrum tests the changed expansion rate, matter-radiation equality, sound horizon, damping scale, and neutrino anisotropic stress. Finally, large-scale structure of the universe and the matter power spectrum test the altered equality scale and neutrino free streaming. These observables distinguish a degenerate-neutrino cosmology from the standard thermal relic scenario in complementary epochs.