We have shown that in the context of the standard model of particles, the weak interaction of cosmic microwave background (CMB) and cosmic neutrino background (C\nuB), in 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 current experimental data, significant information can be extracted about the nature of C\nuB which the contribution of CMB-C\nuB forward scattering for TB, TE, and EB power spectra in the case of C\nuB as Majorana particles is twice larger than in the case of Dirac one. Finally, we shortly discuss evidence of cosmic neutrino background in the Planck 2018 polarization data which is reported on a new measurement of the Cosmic Birefringence (CB) angle \beta. It is shown that the mean opacity due to cosmic neutrino background can behave as a birefringent medium changing the linear polarization rotation angle. CB angle is estimated \beta|_{C\nu B}\simeq 4.5deg in the case of C\nuB as Dirac particles. However this value for \beta is one order larger than the reported value by other studies, but there is no need to worry because \sin(2\beta)<0.2 (\sin(2\beta)<0.35) in the case Dirac (Majorana) neutrinos which is consistent with current experimental data for C_l^{(EB)}.
