NEUTRINO ENERGY LOSS AT MATTER-RADIATION DECOUPLING PHASE

Neutrinos are produced copiously in the early universe. Neutrinos and antineutrinos ceased to be in equilibrium with radiation when the weak interaction rate becomes slower than the rate expansion of the universe. The ratio of the temperature of the photon to the temperature of the neutrino at this stage is T_γ/T_ν = (11/4)^1/3. We investigate the neutrino energy loss due to the oscillation of the electron neutrino into a different flavor in the charged-current interaction of ν_e-e^- based on the work of Sulaksono and Simanjuntak. The energy loss from the neutrinos ΔE_ν during the decoupling of the neutrinos with the rest of the matter would be a gain in the energy of the electrons and can be obtained from the integration of stopping power equation ΔE_ν = (dE_ν/dT^-1)dT^-1 where E_ν and T are the energy of the neutrinos and the temperature respectively. When the universe expands and matter-radiation decouples, an extra energy will be transferred to the photons via the annihilation of the electron-positron pairs, e⁺+e^-→γ+γ. This consequently will increase the temperature of the photons. The net effect to the lowest order is an increase in the ratio of the photon temperature to the neutrino temperature. The magnitude of energy loss of the neutrino is ∼10^-4-10^-5 MeV for the probability of conversion of ν_e → ν_i (i = μ,τ) between 0 to 1.0.