It is shown that in the context of the standard model of particles, weak interaction of cosmic microwave background (CMB) and cosmic neutrino background (CnB), in the order of one loop forward scattering, can generate non-vanishing TB and EB power spectra in the presence of scalar perturbation which is in contrast with the standard scenario cosmology. By comparing our results with the current experimental data, significant information can be extracted about the nature of CnB: the contribution of CMB-CnB forward scattering for TB, TE, and EB power spectra in the case of CnB as Majorana particles is twice larger than that in the case of Dirac one. Finally, we have discussed the evidence of cosmic neutrino background in the Planck 2018 polarization data reported on a new measurement of the cosmic birefringence (CB) angle b. It is shown that the mean opacity due to cosmic neutrino background can behave as an anisotropic birefringent medium changing the linear polarization rotation angle. Despite the good agreement of our results with the reported data (for EB power spectrum), CB angle from the average value of beta=1/2k¯is about two (four) times larger than what reported in [40], in the case of CnB as Dirac (Majorana) particles. This point will be discussed more precisely.