Neutrino effects in cosmology with A primordial magnetic field

If a primordial magnetic field was present during photon decoupling and afterward, a finite neutrino mass could affect the Cosmic Microwave Background (CMB). In previous work [1], we studied the effect of a neutrino mass on the vector and tensor modes of the CMB power spectra. In this work, we also calculated the scalar mode and found that a neutrino mass also has a large effect on it. We decomposed the scalar, vector and tensor modes into Integrated Sachs-Wolfe (ISW), polarization (Pol), doppler (Dop) and Sachs-Wolfe (SW) components, and studied which components are affected strongly by the neutrino mass. We found that a cancellation among neutrino effects on these components offsets each other and the total effect becomes small.