Differential neutrino heating and reduced $^4$He production from decaying particles in the early universe

Abstract

A decaying particle that dominates the energy density of the universe and then decays with a lifetime $\sim 10^{-1}$ sec into electromagnetically-interacting particles can heat the background electron neutrinos more than the $μ$ and $τ$ neutrinos, resulting in a decrease in the primordial $^4$He abundance. Previous calculations of this effect assumed sudden decoupling of the neutrinos from the electromagnetic plasma. Here we repeat this calculation using an improved (although still approximate) treatment of the energy flow from the blackbody radiation into the various neutrino components. We find that with our improved calculation, the reduction in the primordial $^4$He is not as large as had been previously thought, but it occurs over a larger range in decaying particle lifetime $τ$. The reduction in $^4$He can be as large as $ΔY = -0.01$ for $τ= 0.1 - 0.7$ sec.