A CMB Search for the Neutrino Mass Mechanism and its Relation to the $H_0$ Tension

Abstract

The majoron, a pseudo-Goldstone boson arising from the spontaneous breaking of global lepton number, is a generic feature of many models intended to explain the origin of the small neutrino masses. In this work, we investigate potential imprints in the Cosmic Microwave Background (CMB) arising from massive majorons, should they thermalize with neutrinos after Big Bang Nucleosynthesis via inverse neutrino decays. We show that Planck2018 measurements of the CMB are currently sensitive to neutrino-majoron couplings as small as $λ\sim 10^{-13}$, which if interpreted in the context of the type-I seesaw mechanism correspond to a lepton number symmetry breaking scale $v_L \sim \mathcal{O}(100) \, {\rm GeV}$. Additionally, we identify parameter space for which the majoron-neutrino interactions, collectively with an extra contribution to the effective number of relativistic species $N_{\rm eff}$, can ameliorate the outstanding $H_0$ tension.

Figures (10)

• Figure 1: Majoron parameter space. The left and right vertical axes correspond to the majoron-neutrino coupling and the scale at which lepton number is spontaneous broken in the type-I seesaw model respectively. Current constraints from KamLAND-Zen Gando:2012pj, BBN (see text), and SN1987A Kachelriess:2000qcFarzan:2002wx are shown in grey. The pink region demarcates parameter space for which the majoron fully thermalizes after neutrino decoupling, leading to $\Delta N_{\rm eff} = 0.11$. The green band highlights the region of parameter space in which the majoron mass could arise from dim-5 Planck suppressed operators \ref{['eq:mass_maj']}. Shown in blue is the parameter space excluded in this work using Planck2018 data at 95% CL. The parameter space below the black dotted line is excluded if there was a small but primordial population of thermal majorons. The region labeled '$H_0$' is the preferred $1\sigma$ contour for resolving the Hubble tension.
• Figure 2: $H_0$ posteriors for $\Lambda$CDM (black), $\Lambda$CDM + $\Delta N_{\rm eff}$ (blue), and majoron + $\Delta N_{\rm eff}$ (red), using Planck2018 + BAO (solid) and including a gaussian likelihood for SH$_0$ES (dashed). SH$_0$ES posterior shown for comparison in green. See Table \ref{['table:param_values']} for best-fit values and $1\sigma$ uncertainties. The red solid line roughly corresponds to $H_0 = 68.0 \pm 1.9$ km/s/Mpc and hence is in $2.5\sigma$ tension with the SH$_0$ES measurement.
• Figure S1: Left panel: Ratio of majoron-neutrino interaction rate to Hubble expansion rate. Right panel: Majoron energy density evolution as a function of the interaction strength.
• Figure S2: Left: Evolution of the joint neutrino-majoron energy density. Right: Evolution of both the equation of state (solid) and speed of sound (dashed) for a majoron with $m_\phi = 1$ keV and various interaction strengths, with both normalized via a multiplicative factor of 3 such that for radiation $3 \times \omega = 3 \times c_s^2 = 1$. Black curves in both panels denote the $\Lambda$CDM values.
• Figure S3: Percent difference between the TT (left) and EE (right) power spectrum for a $1$ eV majoron with various values of $\Gamma_{\rm eff}$. One sigma errors from Planck 2018 are shown in gray.