Neutrino Mass Spectrum and Future Beta Decay Experiments

We study the discovery potential of future beta decay experiments on searches for the neutrino mass in the sub-eV range, and, in particular, KATRIN experiment with sensitivity $m > 0.3$ eV. Effects of neutrino mass and mixing on the beta decay spectrum in the neutrino schemes which explain the solar and atmospheric neutrino data are discussed. The schemes which lead to observable effects contain one or two sets of quasi-degenerate states. Future beta decay measurements will allow to check the three neutrino scheme with mass degeneracy, moreover, the possibility appears to measure the CP-violating Majorana phase. Effects in the four neutrino schemes which can also explain the LSND data are strongly restricted by the results of Bugey and CHOOZ oscillation experiments: Apart from bending of the spectrum and the shift of the end point one expects appearance of small kink of ($< 2$) size or suppressed tail after bending of the spectrum with rate below 2 % of the expected rate for zero neutrino mass. We consider possible implications of future beta decay experiments for the neutrino mass spectrum, the determination of the absolute scale of neutrino mass and for establishing the nature of neutrinos. We show that beta decay measurements in combination with data from the oscillation and double beta decay experiments will allow to establish the structure of the scheme (hierarchical or non-hierarchical), the type of the hierarchy or ordering of states (normal or inverted) and to measure the relative CP-violating phase in the solar pair of states.Comment: 48 pages, LaTeX, 8 figures, typos removed, references and discussion of the supernova neutrino bounds adde

Searching for dark matter isocurvature initial conditions with N-body Simulations

Small fraction of isocurvature perturbations may exist and correlate with adiabatic perturbations in the primordial perturbations. Naively switching off isocurvature perturbations may lead to biased results. We study the effect of dark matter isocurvature on the structure formation through N-body simulations. From the best fit values, we run four sets of simulation with different initial conditions and different box sizes. We find that, if the fraction of dark matter isocurvature is small, we can not detect its signal through matter power spectrum and two point correlation function with large scale survey. However, the halo mass function can give an obvious signal. Compared to 5% difference on matter power spectrum, it can get 37% at $z = 3$ on halo mass function. This indicates that future high precise cluster count experiment can give stringent constraints on dark matter isocurvature perturbations.Comment: 6 pages, 4 figure