Cross-correlation power spectra and cosmic birefringence of the CMB via photon-neutrino interaction

In the context of standard model particles, weak interaction cosmic microwave background (CMB) and neutrino (C$\nu$B), can generate non-vanishing TB EB power spectra in order one loop forward scattering, presence scalar perturbation, which is contrast with scenario cosmology. Comparing our results current experimental data may provide, significant information about nature C$\nu$B, including CMB-C$\nu$B scattering for TB, TE, spectra. To this end, different cases were studied, Majorana C$\nu$B Dirac C$\nu$B. On other hand, it was shown that mean opacity due to could behave as an anisotropic birefringent medium change linear polarization rotation angle. Considering contributions from anti-neutrino CMB photons (in case neutrino), we introduce relative density asymmetry ($\delta_\nu=\frac{\Delta n_\nu}{n_\nu}=\frac{n_\nu-n_{\bar{\nu}}}{n_\nu}$). Then, using birefringence angle reported by Planck release $\beta=0.30^\circ\pm0.11^\circ$ ($68\%C.L.$), some constraints be put on $\delta_\nu$. Also, value estimated at $\beta|_\nu\simeq0.2$ rad. respect, since are exactly same, both CB will added together. However, least two orders larger than release, ($68\%C.L.$).