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 .
Our results states that the quantum mixing associated to decoherence effects are fundamental for producing an additive quantum entropy contribution to the cosmological neutrino thermal history .
According to our framework , it does not modify the predictions for the number of neutrino species , N _ { \nu } \approx 3 .
It can only relieve the constraints between N _ { \nu } and the neutrino to radiation temperature ratio , T _ { \nu } / T _ { \gamma } , by introducing a novel ingredient to re-direct the interpretation of some recent tantalizing evidence than N _ { \nu } is significantly larger than by more than 3 .