Neutrino masses in astroparticle physics - MPP Theory Group

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702 G.G. Raffelt / New Astronomy Reviews 46 (2002) 699–708Fig. 1. Power spectrum of the galaxy distribution function measured by the 2dF Galaxy Redshift Survey. The solid line is the theoreticalprediction without neutrino dark matter (Vn 50), the dashed line for Vn 50.01, and dot-dashed for Vn50.05. The other cosmological2parameters are V 50.3, V 50.7, h 5 0.70, and V h 5 0.02. [Figure from Elgaroy et al. (2002) with permission.]M L BSky Survey will have greater sensitivity to the a hot dark matter component can be related to eachoverall shape of PGal(k) on the relevant scales, other if the cosmic neutrino density nnis known.allowing one to disentangle more reliably the impact However, the cosmic neutrino background cannot beof b and V on P (k). It is foreseen that one can measured with foreseeable methods so that onen Mreach a sensitivity of om | 0.65 eV (Hu et al., depends on indirect arguments for determining nn.n1998).Even if we accept that there are exactly three0For a degenerate neutrino mass scenario the limit neutrino flavors as indicated by the Z decay widthof Eq. (4) corresponds to a limit on the overall mass and that they were once in thermal equilibrium doesscale of m , 0.8 eV, far more restrictive than the not fix nn. Each flavor is characterized by annlaboratory limit Eq. (2). However, the KATRIN unknown chemical potential mnor a degeneracyproject for improving the tritium endpoint sensitivity parameter jn 5 mn/T, the latter being a quantityis foreseen to reach the 0.3 eV level (Osipowicz, invariant under cosmic expansion. While the ob-2001), similar to the anticipated sensitivity of future served baryon-to-photon ratio suggests that the decosmologicalobservations. If both methods yield a generacy parameters of all fermions are very small,positive signature, they will mutually re-enforce each for neutrinos this is an assumption and not another. If they both find upper limits, again they will established fact.be able to cross-check each other’s constraints.In the presence of a degeneracy parameter jnthenumber and energy densities of relativistic neutrinosplus anti-neutrinos in thermal equilibrium are3. How many neutrinos in the universe? 2 433z3 2ln(2) jnjn6nn 5 Tn]] 2 F1 1]]] 1]]1O(jn) G,The laboratory limits or future measurements of2p 3z3 72 z3mnand the cosmological limits or future discovery of (5)
4 ]]F ]S]D ]S]DGG.G. Raffelt / New Astronomy Reviews 46 (2002) 699–708 7032 2 47p 30 j 15 jwithin about 1%. In that case the relation between Vnnnrn 5 Tn1 1 1 . (6) and mnis uniquely given by the standard expression120 7 p 7 pEq. (1).Therefore, if chemical potentials are taken to be the The approach to flavor equilibrium in the earlyonly uncertainty of the cosmic neutrino density, nnuniverse by neutrino oscillations and collisions wascan only be larger than the standard value. In this recently studied by Lunardini and Smirnov (2001),sense the structure formation limits on the hot dark Dolgov et al. (2002), Wong (2002), and Abazajian etmatter fraction provide a conservative limit on the al. (2002). Assuming the atmospheric and solarneutrino mass scale mn. Conversely, a laboratory LMA solutions, an example for the cosmic flavorlimit on mndoes not limit the hot dark matter evolution is shown in Fig. 2. The detailed treatmentfraction while a positive future laboratory measure- is rather complicated and involves a number ofment of mnprovides only a lower limit on Vn. subtleties related to the large weak potential causedBig-bang nucleosynthesis (BBN) is affected by rnby the neutrinos themselves as they oscillate. Thein that a larger neutrino density increases the primor- intriguing phenomenon of synchronized flavor oscildialexpansion rate, thereby increasing the neutron- lations (Samuel, 1993; Pastor et al., 2001) plays anto-proton freeze-out ratio n/p and thus the cosmic important and subtle role.helium abundance. Therefore, the observed helium The practical bottom line, however, is ratherabundance provides a limit on rnwhich corresponds simple. Effective flavor equilibrium before n/pto some fraction of an effective extra neutrino freeze-out is reliably achieved if the solar oscillationspecies. In addition, however, an electron neutrino parameters are in the favored LMA region. In thechemical potential modifies n/p ~ exp(2jn e). De- LOW region, the result depends sensitively on thepending on the sign of jn ethis effect can increase or value of the small but unknown third mixing angledecrease the helium abundance and can compensate Q13. In the SMA and VAC regions, which are nowfor the r effect of other flavors (Kang and Steig- heavily disfavored, equilibrium is not achieved.nman, 1992). If jn eis the only chemical potential, Therefore, establishing LMA as the correct solutionBBN provides the limitof the solar neutrino problem amounts in our context2 0.01 , j , 0.07. (7)n eIncluding the compensation effect, the only upperlimit on the radiation density comes from precisionmeasurements of the power spectrum of the temperaturefluctuations of the cosmic microwave backgroundradiation and from large-scale structure measurements.A recent analysis yields the allowedregions (Hansen et al., 2002)2 0.01 , j , 0.22 , uj u , 2.6 , (8)nenm,tto counting the number of cosmological neutrinosand thus to establishing a unique relationship betweenthe neutrino mass scale mnand the cosmicneutrino density Vn. A final confirmation of LMA isexpected by the Kamland reactor experiment (Shirai,2002) within the next few months of this writing.4. Z-burst scenario for the highest-energycosmic raysin agreement with similar results of Hannestad The number density and mass of cosmic back-(2001) and Kneller et al. (2001). ground neutrinos is also relevant for the propagationHowever, the observed neutrino oscillations imply of extremely high-energy (EHE) neutrinos that maythat the individual flavor lepton numbers are not be produced by hitherto unknown astrophysicalconserved and that in true thermal equilibrium all sources at cosmological distances. Assuming thatneutrinos are characterized by one single chemical21 22neutrinos with energies in the 10 –10 eV range arepotential jn. If flavor equilibrium is achieved before somewhere injected in the universe, and assumingn/p freeze-out the restrictive BBN limit on jn ethat the cosmic background neutrinos have masses inapplies to all flavors, i.e. ujnu , 0.07, implying that the neighborhood of 1 eV, the center-of-momentum0the cosmic number density of neutrinos is fixed to energy is in the neighborhood of the Z boson mass.
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