Majoron Light Relics: Lifetimes, Decay Radiation and Production in a Capped Thermal Bath

For a breaking scale of 10^5 GeV and a mass of 1 keV the lifetime is 4.41e+13 seconds, well inside the early universe, so such a majoron decays while its decay products can still affect the radiation history and nucleosynthesis. At 10^7 GeV the lifetime reaches 4.41e+17 seconds, comparable to the age of the universe at 4.35e+17 seconds, and at 10^9 GeV it stretches to 4.41e+21 seconds, far beyond the present age, so that population would survive as a relic. A heavier majoron of 10 keV at the lowest breaking scale decays after only 4.41e+12 seconds. The bound density of 9.72e+54 g per cubic centimetre guarantees a thermal bath hot enough to produce all of these cases, so production cannot be evaded by appealing to a cooler beginning. This study is computed from stated assumptions and published comparison values; it is not a measurement.