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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.
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Kahniashvili et al. (2007) studied this question.
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