Neutrino mass effects on vector and tensor CMB anisotropies in the presence of a primordial magnetic field

Abstract

If a primordial magnetic field (PMF) is present during photon decoupling and afterward, a finite neutrino mass can affect all modes of the CMB. In this work, we expand on earlier studies of the scalar mode effects by constructing the vector and tensor mode equations in the presence of massive neutrinos and a PMF. We compute the power spectrum of the various modes in an illustrative example and find that the neutrino mass can significantly affect the vector and tensor modes when a PMF exists, while the effects are negligible for no PMF. The most prominent result of the present analysis is the behavior of the EE component of the tensor mode at low multipoles. For massive neutrinos the EE mode can become comparable to the observed primary anisotropy. Therefore, if and when the EE mode power spectrum is measured at low multipoles the possibility exists to place a strong constraint on the sum of the neutrino masses.

arXiv comment11 pages, 8 figures

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• Massive Neutrinos and Magnetic Fields in the Early Universe
• New Constraints on the Primordial Magnetic Field
• The Search for a Primordial Magnetic Field
• Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations
• Effects of helical magnetic fields on the cosmic microwave background
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• Generation of Curvature Perturbations with Extra Anisotropic Stress
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• Impact of a primordial magnetic field on cosmic microwave background $B$ modes with weak lensing