Cosmological neutrino bounds for non-cosmologists
  I briefly review cosmological bounds on neutrino masses and the underlying gravitational physics at a level appropriate for readers outside the field of cosmology. For the case of three massive neutrinos with standard model freezeout, the current 95% upper limit on the sum of their masses is 0.42 eV. I summarize the basic physical mechanism making matter clustering such a sensitive probe of massive neutrinos. I discuss the prospects of doing still better in coming years using tools such as lensing tomography, approaching a sensitivity around 0.03 eV. Since the lower bound from atmospheric neutrino oscillations is around 0.05 eV, upcoming cosmological measurements should detect neutrino mass if the technical and fiscal challenges can be met. 
Max Tegmark