Constraining MeV to 10 GeV majoron by Big Bang Nucleosynthesis

We estimate the Big Bang nucleosynthesis (BBN) constraint on the majoron in the mass range between $1\,{\rm MeV}$ to $10\,{\rm GeV}$ which dominantly decays into the standard model neutrinos. When the majoron lifetime is shorter than $1\,{\rm sec}$, the injected neutrinos mainly heat up background plasma, which alters the relation between photon temperature and background neutrino temperature. For a lifetime longer than $1\,{\rm sec}$, most of the injected neutrinos directly contribute to the protons-to-neutrons conversion. In both cases, deuterium and helium abundances are enhanced, while the constraint from the deuterium is stronger than that from the helium. $^7{\rm Li}$ abundance gets decreased as a consequence of additional neutrons, but the parameter range that fits the observed $^7{\rm Li}$ abundance is excluded by the deuterium constraint. We also estimate other cosmological constraints and compare them with the BBN bound.