A cosmological sandwiched window for lepton-number breaking scale

Abstract A singlet majoron can arise from the seesaw framework as a pseudo-Goldstone boson when the heavy Majorana neutrinos acquire masses via the spontaneous breaking of global U(1) L symmetry. The resulting cosmological impacts are usually derived from the effective majoron-neutrino interaction, and the majoron abundance is accumulated through the freeze-in neutrino coalescence. However, a primordial majoron abundance can be predicted in a minimal setup and lead to distinctive cosmological effects. In this work, we consider such a primordial majoron abundance from relativistic freeze-out and calculate the modification to the effective neutrino number N eff . We demonstrate that the measurements of N eff will constrain the parameter space from a primordial majoron abundance in an opposite direction to that from neutrino coalescence. When the contributions from both the primordial abundance and the freeze-in production coexist, the U(1) L -breaking scale (seesaw scale) f will be pushed into a “sandwiched window”. Remarkably, for majoron masses below 1 MeV and above the eV scale, the future CMB-S4 experiment will completely close such a low-scale seesaw window for f ∈ 1,10 5 GeV. We highlight that any new light particle with a primordial abundance that couples to Standard Model particles may lead to a similar sandwiched window, and such a general phenomenon deserves careful investigation.