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.Comment: 4 pages, 2 figs, in "Neutrino Physics", Proceedings of Nobel
Symposium 129, eds., L Bergstrom, O. Botner, P. Carlson, P. O. Hulth, and T.
Ohlsso