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On the basis of the quantum Boltzmann equation governing the time-evolutionof the density matrix of polarized CMB photons in the primordial scalarperturbations of metric, we calculate the B-mode spectrum of polarized CMBphotons contributed from the scattering of CMB photons and CNB neutrinos(Cosmic Neutrino Background). We show that such contribution to the B-modespectrum is negligible for small $\ell$, however is significantly large for $50< \ell< 200$ by plotting our results together with the BICEP2 data. Our studyand results imply that in order to theoretically better understand the originof the observed B-mode spectrum of polarized CMB photons ($r$-parameter), itshould be necessary to study the relevant and dominate processes in both tensorand scalar perturbations.

Photon-neutrino scattering and the B-mode spectrum of CMB photons