Cosmological neutrino entropy changes due to flavor statistical mixing

Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto - Rua do Campo Alegre 687, 4169-007, Porto, Portugal, EU

^(a) On leave of absence from Departamento de Física, Universidade Federal de São Carlos - PO Box 676, 13565-905, São Carlos, SP, Brasil; alexeb@ufscar.br

Received: 13 June 2013
Accepted: 6 August 2013

Abstract

Entropy changes due to delocalization and decoherence effects should modify the predictions for the cosmological neutrino background (CνB) temperature when one treats neutrino flavors in the framework of composite quantum systems. Assuming that the final stage of neutrino interactions with the 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 states. 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. Depending on the quantum measurement scheme used for quantifying the entropy, mixing associated to dissipative effects can lead to an increase of the flavor-associated von Neumann entropy for free-streaming neutrinos. The production of the 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 state 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, . It can only relieve the constraints between and the temperature ratio, , by introducing a novel ingredient to re-direct the interpretation of some recent tantalizing evidence that is significantly larger than by more than 3.