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 $\Delta f=0.046$ is obtained for the model with tensor-to scalar ratio $r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of $B$-polarization, $\Delta f=0.008$ is obtained for the model with $r=0.1$. So the precise observation of the CMB $B$-polarization provides a great opportunity to study the relativistic components in the early Universe.