Cosmological neutrino background revisited

We solve the Boltzmann equation for cosmological neutrinos around the epoch of the electron-positron annihilation in order to verify the freeze-out ap proximation and to compute accurately the cosmological neutrino distributio n function. We find the radiation energy density to be about 0.3% higher th an predicted by the freeze-out approximation. As a result, the spectrum of the cosmic microwave background anisotropies changes by similar to 0.3%-0.5 %, depending on the angular scale, and the amplitude of the mass fluctuatio ns on scales below about 100 h(-1) Mpc decreases by about 0.2%-0.3%.