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Any light relic which was in thermal equilibrium with the Standard Modelbefore it freezes out results in a shift in the effective number of neutrinospecies, $N_{eff}$. This quantity is being measured with increasing precision,and planned experiments would seemingly rule out light particles beyond theStandard Model, even for rather high temperature light particle freeze out.Here we explore how these bounds are loosened if the energy density of thelight particles is diluted with respect to that of Standard Model radiation,which can happen if a heavy particle decays into the Standard Model bath afterthe light particle freezes out. After calculating how heavy state decays alter$N_{eff}$ for light particles beyond the Standard Model, we focus in particularon the case that the heavy decaying particle is a gravitino, and use currentbounds on $N_{eff}$ to place constraints on the gravitino mass and thebranching ratio into light particles for different values of the reheatingtemperature of the Universe.

How Effective is $N_{eff}$ at Discovering Dark Radiation in a Cosmology with Heavy Particle Decay?