CMB anisotropies due to cosmological magnetosonic waves

We study scalar mode perturbations (magnetosonic waves) induced by a helical stochastic cosmological magnetic field and derive analytically the corresponding cosmic microwave background (CMB) temperature and polarization anisotropy angular power spectra. We show that the presence of a stochastic magnetic field, or an homogeneous magnetic field, influences the acoustic oscillation pattern of the CMB anisotropy power spectrum, effectively acting as a reduction of the baryon fraction. We find that the scalar magnetic energy density perturbation contribution to the CMB temperature anisotropy is small compared to the contribution to the CMB $E$-polarization anisotropy.