New method to constrain the relativistic free-streaming gas in the Universe

We discuss a method to constrain the fraction density f of the relativistic gas in the radiation-dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) B-polarization power spectrum. We find that the uncertainty of f   strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty Δf=0.046$\mathrm{\Delta }f=0.046$ is obtained for the model with tensor-to-scalar ratio r=0.1$r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of B  -polarization, Δf=0.008$\mathrm{\Delta }f=0.008$ is obtained for the model with r=0.1$r=0.1$. So the precise observation of the CMB B-polarization provides a great opportunity to study the relativistic components in the early Universe.