A CMB Search for the Neutrino Mass Mechanism and its Relation to the
  $H_0$ Tension
  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 $\lambda \sim 10^{-13}$, 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.
