Rick's Cosmology Tutorial: Chapter 5 Abstract

The black body equations for fermions are used to derive the photon:neutrino temperature ratio after positron annihilation at ~14 seconds. It is 1.40. The black body equations for fermions also permit calculation of the contribution made by the neutrinos to the universe's energy density. This is just 68% of that due to photons, assuming 3 neutrino 'flavours'.

Observational evidence is that dark matter accounts for 25% of the critical density. It is shown that this could be attributed solely to neutrinos if the sum of the neutrino masses were 12eV. Lamentably, the latest bound on the sum of the neutrino masses from WMAP-3 is just 0.6eV. Therefore neutrinos cannot account for more than 5% of the observed dark matter.

Limitations: It has been assumed that neutrinos have only one permitted helicity state. If this is untrue, their contribution to the universal density would be double that calculated herein.

Sun showing solar flare