While it is very difficult to detect the cosmic background of neutrinos directly, there are several experimental approaches that might be able to measure the mass of the neutrino. As I noted earlier, the detection of a stable several eV neutrino would imply that neutrinos comprise a significant fraction of the mass of the universe.
The classical approach to measuring neutrino
mass are measurements of the
decay endpoint. Current limits
from these experiments imply that the electron
neutrino is not the predominant component of the dark matter; however, these
experiments cannot place astrophysically
interesting constraints on the mass of the mu or tau neutrino.
If the neutrino is a Majorana particle, then it might
be indirectly detected through the detection of
a neutrinoless double beta decay. Deep underground
experiments looking for rare decays have
placed very interesting limits [34] on the electron neutrino
mass:
eV.
This is a limit on massive neutrinos
if the most massive eigenstate contains
a significant fraction of the electron flavor eigenstate
and does not apply to all neutro models.
Neutrino oscillation experiments are sensitive
to mass differences, usually
and sometime
. Recent results from
the Los Alamos experiment
[5], which suggest a detection
of neutrino oscillations, are controversial [35].
There is a possibility of an astronomical detection
of neutrino mass using neutrinos from a supernova explosion.
If the neutrinos are massive, then more-energetic neutrinos
arrive earlier than less-energetic neutrinos. Thus,
neutrino detectors would first see higher energy events
and then see less energetic events. This effect was
not observed in SN 1987A, which suggests
that 
eV [64]. Observations of a galactic
supernova by Sudbury detector, which is sensitive
to 
could place interesting limits
on their masses and possibly rule out
neutrinos as cosmologically interesting.