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

Pramana

Swapnil S Jawkar1¹  Sudhanshu S Jha¹ 

[1] Department of Physics, Indian Institute of Technology, Mumbai 400 076, India$$

关键词: Cosmic neutrino background;    relic neutrinos;    mean square fluctuation;    neutrino mass.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Using the general formulation for obtaining chemical potential 𝜇 of an ideal Fermi gas of particles at temperature 𝑇, with particle rest mass $m_{0}$ and average density $langle N angle/V$ , the dependence of the mean square number fluctuation $langle 𝛥 N^{2} angle/V$ on the particle mass $m_{0}$ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energy $m_{0}c^{2}$ is very large (non-relativistic case), very small (ultrarelativistic 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 $langle N_{𝜈} angle/V$ but also the mean square fluctuation $langle 𝛥 N_{𝜈}^{2} angle/V$. 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 $m_{𝜈}$ instead of the actual mass $m_{0𝜈}.

【 授权许可】

Unknown