= Solution
The <density bound on a relativistically decoupled massive relic> is already decisive for a conventional near-critical cosmological density budget: the thermal pair alone gives $\Omega\simeq22.4$. The same additional relativistic pair increases the <effective number of neutrino species> by one during nucleosynthesis and raises the <primordial helium mass fraction>, so its expansion effect supplies another constraint. Thus \b[a stable, fully thermalized MeV-decoupling <neutrino> pair of this mass is incompatible with the usual cosmological density budget].
This conclusion is not a prohibition on every particle with that mass. Earlier decoupling followed by entropy dilution, a reduced production abundance, or interactions that change the assumed thermal history can alter both tests. At fixed mass, requiring this pair to contribute no more than the supplied <critical density> would demand a number density at most $1/22.4$ of the standard value, or a thermal temperature at most $(1/22.4)^{1/3}\simeq0.355$ of the standard <neutrino> temperature. No numerical abundance or exclusion independent of these assumptions follows from the mass and equal particle-antiparticle counts alone.
Back to article page
