The C$\nu$B energy density through the quantum measurement theory

Abstract

We apply concepts from the quantum measurement theory to obtain some cosmological neutrino background (C$\nu$B) properties and discuss their relevance in defining theoretical bounds on cosmological neutrino energy density. Describing three neutrino generations as a composite quantum system through the generalized theory of quantum measurement provides us with the probabilistic correlation between observable energies and neutrino flavor eigenstates. By observing that flavor-averaged and flavor-weighted energies are the quantum observables respectively generated by selective and non-selective quantum measurement schemes, it is possible to identify the constraints on the effective mass value expression that determines the neutrino contribution to the energy density of the cosmic inventory. Our results agree with the quantum mechanics viewpoint that asserts that the cosmological neutrino energy density is obtained from a coherent sum of mass eigenstate energies, for normal and inverted mass hierarchies.

Comments: 19 pages, 5 figures, for completeness, in the Appendix, we have added the contents related to Quantum Measurement schemes reproduced from arXiv:1104.3120 of one of the authors of this manuscript (Alex E. Bernardini). The credits/quotations are consistent and accurately given to arXiv:1104.3120. The authors suggest the reading of arXiv:1104.3120 as a background for the present manuscript