The Abundance of a Light Thermal Relic Computed Against the Limit Density and the Observed Radiation Budget

A relic decoupling at g_* = 106.75 reaches Omega h^2 = 0.12 only at a mass of 1.11e+02 eV, while one decoupling at g_* = 10.75 reaches the same density at 1.12e+01 eV; the protective factor from early decoupling is 9.93e+00. To stay below a hot-component ceiling of 0.001 in Omega h^2, the earliest-decoupled case must be lighter than 9.25e-01 eV. All of these masses are utterly negligible next to the thermal scale at the bound density of 9.72e+54 g per cubic centimetre, which is why the relic is relativistic at decoupling in every case considered. Early decoupling raises the mass compatible with the observed density from 1.12e+01 eV to 1.11e+02 eV. This study is computed from stated assumptions and published comparison values; it is not a measurement.