Neutrino masses in astroparticle physics - MPP Theory Group

G.G. Raffelt / New Astronomy Reviews 46 (2002) 699–708 701dark matter of the universe. However, it soon energy’’). And because neutrinos do have mass, theybecame clear that neutrinos were not a good dark contribute at least 0.1% of the critical density. Thismatter candidate for two reasons. The first argument fraction is based on a hierarchical mass scenario withis based on the limited phase space for neutrinos m35 50 meV, the smallest value consistent withgravitationally bound to a galaxy (Tremaine and atmospheric neutrino oscillations.Gunn, 1979). As a consequence, if massive neutrinos An upper limit on the neutrino dark matter fractionare supposed to be the dark matter in galaxies, they can be derived from the measured power spectrummust obey a lower mass limit of some 30 eV for PM(k) of the cosmic matter distribution. Neutrinotypical spirals, and even 100–200 eV for dwarf free streaming suppresses the small-scale structuregalaxies. by an approximate amount (Hu et al., 1998)Today the most restrictive laboratory limits on theDPMVoverall neutrino mass scale arise from the Mainzn]] ¯ 2 8 ](Weinheimer et al., 1999) and Troitsk (Lobashev et PMVM(3)al., 1999) tritium end-point experiments. The current where VMis the cosmic mass fraction in matter, i.e.limit is (Weinheimer, 2002)excluding the dark energy. This effect is illustratedm , 2.2 eV at 95% CL . (2)nin Fig. 1 where PM(k) measured by the 2dF GalaxyRedshift Survey is shown and compared with thepredictions for a cold dark matter cosmology withneutrino fractions Vn5 0, 0.01, and 0.05, respective-ly (Elgaroy et al., 2002). When the theoretical curvesThis limit applies to all mass eigenstates if we acceptthat the mass differences are as small as indicated bythe atmospheric and solar oscillation interpretation. are normalized to the power at large scales, neutrinosThis limit is so restrictive that neutrinos as galactic indeed suppress PM(k) at large k.dark matter are completely out of the question, even Based on the 2dFGRS data, Elgaroy et al. (2002)without any further appeal to cosmic structure forma- and Hannestad (2002) find limits on omnin thetion arguments.range 1.8–3.0 eV, depending on the assumed priorsHowever, cosmic structure formation does place for other cosmological parameters, notably the Hubpowerfullimits on the neutrino mass. The observed ble constant, the overall matter fraction VM, and thestructure in the distribution of galaxies is thought to tilt of the spectrum of primordial density fluctuaarisefrom the gravitational instability of primordial tions. For a reasonable set of priors one may adoptdensity fluctuations. The small masses of neutrinosimply that they stay relativistic for a long time after O mn, 2.5 eV (4)flavorstheir decoupling (‘‘hot dark matter’’), allowing themto stream freely, thereby erasing the primordial at a statistical confidence level of 95%. This limitdensity fluctuations on small scales (Doroshkevich et corresponds approximately to the dot-dashed (V n5al., 1980). While this effect does not preclude 0.05) curve in Fig. 1, i.e. neutrinos may still contribneutrinodark matter, it implies a top-down scenario ute as much as 5% of the critical density, about asfor structure formation where large structures form much as baryons.first, later fragmenting into smaller ones. It was soon Within the framework of the standard theory ofrealized that the predicted properties of the large- structure formation, the largest systematic uncertainscalematter distribution did not seem to agree with ty comes from the unknown biasing parameter bobservations and that neutrino dark matter was which relates the power spectrum of the galaxyapparently ruled out (White et al., 1983).distribution to that of the true underlying matter2Today it is widely accepted that the universe has distribution, PGal(k) 5 b PM(k). The biasing paramecriticaldensity and that its matter inventory sports ter is one of the quantities which must be taken intoseveral nontrivial components. Besides some 5% account when fitting all large-scale structure data tobaryonic matter (most of it dark) there are some 25% observations of the galaxy distribution and of thecold dark matter in an unidentified physical form and temperature fluctuations of the cosmic microwavesome 70% of a negative-pressure component (‘‘dark background radiation. In the future the Sloan Digital