Cosmological neutrino entropy changes due to flavor statistical mixing

Abstract

Entropy changes due to delocalization and decoherence effects should modify the predictions for the cosmological neutrino background (C$\nu$B) temperature when one treats neutrino flavors in the framework of composite quantum systems. Assuming that the final stage of neutrino interactions with the $\gamma e^{-}e^{+}$ radiation plasma before decoupling works as a measurement scheme that projects neutrinos into flavor quantum states, the resulting free-streaming neutrinos can be described as a statistical ensemble of flavor-mixed neutrinos. Even not corresponding to an electronic-flavor pure state, after decoupling the statistical ensemble is described by a density matrix that evolves in time with the full Hamiltonian accounting for flavor mixing, momentum delocalization and, in case of an open quantum system approach, decoherence effects. Since the statistical weights, $w$, shall follow the electron elastic scattering cross section rapport given by $0.16\,w_{e} = w_{\mu} = w_{\tau}$, the von-Neumann entropy will deserve some special attention. Depending on the quantum measurement scheme used for quantifying the entropy, mixing associated to dissipative effects can lead to an increasing of the flavor associated von-Neumann entropy for free-streaming neutrinos. The production of von-Neumann entropy mitigates the constraints on the predictions for energy densities and temperatures of a cosmologically evolving isentropic fluid, in this case, the cosmological neutrino background. The effects of entropy changes on the cosmological neutrino temperature are quantified, and the {\em constraint} involving the number of neutrino species, $N_{\nu} \approx 3$, in the phenomenological confront with Big Bang nucleosynthesis parameters is consistently relieved.