Probing the effective number of neutrino species with the cosmic microwave background

We discuss how much we can probe the effective number of neutrino species N_ with the cosmic microwave background alone. Using the data of the WMAP, ACBAR, CBI, and BOOMERANG experiments, we obtain a constraint on the effective number of neutrino species as 0. 96<N_<7. 94 at 95% C. L. for a power-law flat universe model. The limit is improved to be 1. 39<N_<6. 38 at 95% C. L. if we assume that the baryon density, N_, and the helium abundance are related by the big bang nucleosynthesis theory. We also provide a forecast for the Planck experiment using a Markov chain Monte Carlo approach. In addition to constraining N_, we investigate how the big bang nucleosynthesis relation affects the estimation for these parameters and other cosmological parameters.