= Solution
<Standard Model> active <neutrinos> decouple while relativistic and retain a thermal momentum distribution. They therefore constitute <hot dark matter> for the light masses compatible with the standard cosmological picture. Their <collisionless free streaming> erases <linear cosmological density perturbations> below a characteristic scale. Making them the dominant gravitating matter would delay small-scale structure formation and suppress the observed <matter power spectrum>.
For standard thermal abundances and nonrelativistic <neutrinos> today,
$$
\Omega_\nu h^2\simeq\frac{\sum_i m_{\nu_i}}{93\ \mathrm{eV}/c^2},
\qquad
h=\frac{H_0}{100\ \mathrm{km\,s^{-1}\,Mpc^{-1}}}.
$$
Increasing the <mass> sum enough to provide all the stipulated <dark matter> conflicts with the successful <cold dark matter> description of cosmological structure. Independently, the <Tremaine-Gunn bound> on the fermionic phase-space occupation limits the density light <neutrinos> can supply in small galactic haloes.<Dynamical Role of Light Neutral Leptons in Cosmology by Scott Tremaine and James Edward Gunn>[Pages 407–410, collisionless phase-space bound]{ref} Oscillations establish nonzero <neutrino mass> differences, but do not make the relic <neutrinos> cold. \b[Active <neutrinos> can contribute some matter; they cannot supply the dominant cold component.] A heavier <sterile neutrino> candidate would be a different hypothesis, not an ordinary <Standard Model> relic.
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