Since we are discussing neutrinos, I thought it is fun to mention antropic
constraints on neutrino masses derived by Tegmark, see here:

Anthropic predictions for neutrino masses
Authors: Max Tegmark (MIT), Alexander Vilenkin (Tufts), Levon Pogosian
Categories: astro-ph
Comments: Revised to match accepted PRD version. Added references,
discussion of very heavy neutrinos, analytic growth factor fit. 9 pages, 4
figs. Color figs and links at this http URL
Journal-ref: Phys.Rev. D71 (2005) 103523

It is argued that small values of the neutrino masses may be due to
anthropic selection effects. If this is the case, then the combined mass of
the three neutrino species is expected to be ~1eV, neutrinos causing a
non-negligible suppression of galaxy formation.

Anthropic predictions for vacuum energy and neutrino masses
Authors: Levon Pogosian, Alexander Vilenkin, Max Tegmark
Categories: astro-ph gr-qc hep-th
Comments: 9 pages, 4 figures
Journal-ref: JCAP 0407 (2004) 005

It is argued that the observed vacuum energy density and the small values of
the neutrino masses could be due to anthropic selection effects. Until now,
these two quantities have been treated separately from each other and, in
particular, anthropic predictions for the vacuum energy were made under the
assumption of zero neutrino masses. Here we consider two cases. In the
first, we calculate predictions for the vacuum energy for a fixed (generally
non-zero) value of the neutrino mass. In the second we allow both quantities
to vary from one part of the universe to another. We find that the anthropic
predictions for the vacuum energy density are in a better agreement with
observations when one allows for non-zero neutrino masses. We also find that
the individual distributions for the vacuum energy and the neutrino masses
are reasonably robust and do not change drastically when one adds the other

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