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

Abstract

We discuss how much we can probe the effective number of neutrino species ${N}_{\ensuremath{\nu}}$ 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 $0.96l{N}_{\ensuremath{\nu}}l7.94$ at 95% C.L. for a power-law $\ensuremath{\Lambda}\mathrm{CDM}$ flat universe model. The limit is improved to be $1.39l{N}_{\ensuremath{\nu}}l6.38$ at 95% C.L. if we assume that the baryon density, ${N}_{\ensuremath{\nu}}$, 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 ${N}_{\ensuremath{\nu}}$, we investigate how the big bang nucleosynthesis relation affects the estimation for these parameters and other cosmological parameters.