13.4 | Neutrinos and the critical density

Assume neutrinos have mass $m_\nu=10^{-5}m_e$. Calculate the neutrino number density needed to account for the Universe's dark matter. Assume a flat universe with 25% of its mass in dark matter.

Take the classical total energy equal to zero. For the numerical evaluation use $H_0=75\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, with $m_e=9.11\times10^{-31}\,\mathrm{kg}$ and $G=6.674\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}$.