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

TL;DR

This paper investigates how finite neutrino mass influences vector and tensor CMB anisotropies in the presence of a primordial magnetic field, highlighting potential for constraining neutrino masses through low-multipole EE mode measurements.

Contribution

It extends previous scalar mode studies by deriving vector and tensor mode equations with massive neutrinos and a primordial magnetic field, and analyzes their impact on CMB power spectra.

Findings

Neutrino mass significantly affects vector and tensor modes with a primordial magnetic field.

The EE component of tensor modes can become comparable to primary anisotropies at low multipoles.

Measuring low-multipole EE spectrum could constrain the sum of neutrino masses.

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.