Cosmology and Neutrino Masses

The first day of the ENTApP Dark Matter Workshop was dominated by the neutrino dark matter. According to the standard cosmological model, there should be relic neutrinos flying around in a number comparable to that of the CMB photons. Neutrinos count as hot dark matter: they were relativistic at the moment they decoupled from the photon plasma. It is impossible that they account for all dark matter in the universe. But it is conceivable they constitute some non-negligible fraction of the total energy density today. The simple formula for the neutrino energy density

tells that cosmology is sensitive to the sum of the neutrino masses. This is just perfect since the neutrino oscillations experiments are sensitive only to differences of the neutrino masses squared. Cosmology provides us with an opportunity to pinpoint the overall scale of neutrino masses!

To achieve this we need to find the characteristic imprints that the cosmic neutrinos leave on large scale structures in the universe. This subject was discussed by Julien Lesgourgues who knows everything about structure formation. His speech was easy and clear, even though his name could suggest otherwise. There was also a related talk by Steen Hannestad.

Neutrinos are practically collisionless. As long as they remain relativistic they free-stream. This means they tend to wipe out dark matter perturbations at scales shorter than the free- streaming length. The latter is simply related to the relic neutrino energy density. Thus, by measuring the distribution of dark matter in the universe we can find out how much neutrino component it contains.

Cosmologists are lucky bastards. Since many years they've been enjoying a constant inflow of new experimental data and they expect much more in near future. The current knowledge about the dark matter distribution at various scales comes from the CMB (WMAP), galaxy surveys (2dF, SDSS), observations of weak gravitational lensing and quasar absorption spectra. Collecting data from various experiments one can draw cool plots like this one stolen from Max Tegmark:
The solid curve is the prediction of a model with cold dark matter only. The relic neutrinos would like to suppress the density fluctuations on the left-hand side of the plot. The effect would be 60% for 1eV neutrinos and 3% for 0.05 eV neutrinos. The current data are good enough to set the bound

which is only an order of magnitude away from the lower limit 0.05 eV set by the oscillation experiments.

The future is bright for dark matter. New experiments will soon provide more accurate data (Planck for the CMB, SDSS-II for galaxy surveys). Weak lensing will tell us about the time evolution of the dark matter power spectrum (see the recent article about weak lensing tomography in Nature). All this will increase the sensitivity to neutrino masses down to 0.1 eV level.

To learn more, there is a comprehensive review Julien made for Physics Reports. If you need something lighter to read on a train, take a look at this article by Steen.