Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Details Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Jan 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005prama..64...17j&link_type=abstract

Pramana, vol. 64, Issue 1, p.17

Physics

1

Cosmic Neutrino Background, Relic Neutrinos, Mean Square Fluctuation, Neu-

Scientific paper

Using the general formulation for obtaining chemical potential mu of an ideal Fermi gas of particles at temperature T, with particle rest mass m_0 and average density < Nrangle/V, the dependence of the mean square number fluctuation < Delta N^2rangle/V on the particle mass m_0 has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energy m_0c^2 is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_{B}T. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density < N_{nu}rangle/V but also the mean square fluctuation < Delta N^2_{nu}rangle/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino mass m_{nu} instead of the actual mass m_{0nu}.

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