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 approximation and to compute accurately the cosmological neutrino distribution function. We find the radiation energy density to be about 0.3% higher than predicted by the freeze-out approximation. As a result, the spectrum of the cosmic microwave background anisotropies changes by ~0.3%-0.5%, depending on the angular scale, and the amplitude of the mass fluctuations on scales below about 100 h -1 Mpc decreases by about 0.2%-0.3%.