CMB Signals of Neutrino Mass Generation

TL;DR

The paper proposes a cosmological probe of neutrino mass generation based on low-scale spontaneous breaking of lepton-flavor symmetries, which yields light pseudo-Goldstone bosons that interact with neutrinos. It identifies two primary CMB observables, ΔNν (relativistic energy density) and Δln (neutrino-scattering-induced peak shifts), and develops a framework to compute these signals across Majorana/Dirac cases and various mass hierarchies. By analyzing minimal models (e.g., U(1)L) and more complex multi-PGB scenarios, the authors map out regions in parameter space (f, mG) where either energy-density or scattering signals are observable, accounting for BBN and astrophysical constraints. They illustrate how Planck and future CMB experiments could distinguish neutrino mass patterns and test low-energy mechanisms such as a low-energy seesaw or SU(3)×U(1)L structures, highlighting the potential richness of phenomenology when multiple PGBs are present and SUSY can naturally realize the required scales.

Abstract

We propose signals in the cosmic microwave background to probe the type and spectrum of neutrino masses. In theories that have spontaneous breaking of approximate lepton flavor symmetries at or below the weak scale, light pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis and affect the acoustic oscillations of the electron-photon fluid during the eV era. Deviations from the Standard Model are predicted for both the total energy density in radiation during this epoch, ΔN_nu, and for the multipole of the n'th CMB peak at large n, Δl_n. The latter signal is difficult to reproduce other than by scattering of the known neutrinos, and is therefore an ideal test of our class of theories. In many models, the large shift, Δl_n \approx 8 n_S, depends on the number of neutrino species that scatter via the pseudo-Goldstone boson interaction. This interaction is proportional to the neutrino masses, so that the signal reflects the neutrino spectrum. The prediction for ΔN_nu is highly model dependent, but can be accurately computed within any given model. It is very sensitive to the number of pseudo-Goldstone bosons, and therefore to the underlying symmetries of the leptons, and is typically in the region of 0.03 < ΔN_nu < 1. This signal is significantly larger for Majorana neutrinos than for Dirac neutrinos, and, like the scattering signal, varies as the spectrum of neutrinos is changed from hierarchical to inverse hierarchical to degenerate.

Figures (4)

• Figure 1: Signal regions and cosmological bounds for a single Majorana neutrino coupled to a single pseudo-Goldstone boson. The lines and regions are labeled as in the text. CMB signals occur throughout the two shaded regions. The area below $f_3$ and $f_4$ is excluded by BBN, and in the region above $f_1$ and $f_2$ the PGB is too weakly coupled to give any signal. There is an energy density signal in region I and a scattering signal in region II. We have assumed $m_\nu = 0.05$ eV $\lambda = 1$.
• Figure 2: Signal regions and cosmological bounds for a single Dirac neutrino coupled to a single pseudo-Goldstone boson. The region below line $f_4$ is exclude by BBN. In the region above lines $f_1$ and $f_2$ the Goldstone boson is too weakly coupled to give any signal. There is a signal in $\rho_{rel}$ in region I, and in region II there is an overall phase shift. We have assumed $m_\nu = 0.05$ eV, $\lambda=1$ and $r=0.0001$. The lower bound on $f$ scales as $f_4 \propto r^{1/3}$.
• Figure 3: The signal regions and bounds for three Majorana neutrinos with hierarchical masses $m_\nu = 0.05, 0.008, 0.002$ eV. The regions are labeled by the number of neutrinos species that recouple to the pseudo-Goldstone boson for $m_G>1$ eV and by the number of neutrinos that scatter at $T \sim 1$ eV for $m_G < 1$ eV.
• Figure 4: The signal regions and bounds for three Dirac neutrinos with hierarchical masses $m_\nu = 0.05, 0.008, 0.002$ eV. The regions are labeled by the number of neutrinos species that recouple to the pseudo-Goldstone boson for $m_G>1$ eV and by the number of neutrinos that scatter at $T \sim 1$ eV for $m_G < 1$ eV and $r=0.0001$.