Can cosmic neutrinos induce a cosmic birefringence signal?

Abstract

A coupling of photons to the cosmic neutrino asymmetry current has been proposed to explain the hinted isotropic rotation of CMB polarization. Gauge invariant UV completions require a Kalb-Ramond field that is exactly dual to a massless axion. We show that, in this case, the product of the axion-photon coupling and the axion-neutrino current coupling is fixed by the signal, $g_{aγ}/f_\ell=1/Λ_*^2$ with $Λ_*\simeq10$ TeV. Using $SU(2)_L$ gauge invariance we show that the dual axion couples to electrons as $g_{aγ}g_{ae}=m_e/Λ_*^2\simeq5\times10^{-12}\,\mathrm{GeV}^{-1}$. This value is excluded by the measured electron magnetic moment combined with light-shining-through-a-wall searches, as well as by stellar evolution. Conserved anomaly-free currents may evade these bounds, but then either a contact interaction among SM fermions excludes the model, or the relic neutrinos decouple from the signal. We conclude that cosmic neutrinos cannot induce a birefringence signal.