Daughters mimic sterile neutrinos (almost!) perfectly

Since only recently, cosmological observations are sensitive to hot dark matter (HDM) admixtures with sub-eV mass, m(hdm)(eff) < eV, that are not fully-thermalised, Delta N-eff < 1. We argue that their almost automatic interpretation as a sterile neutrino species is neither from theoretical nor practical parsimony principles preferred over HDM formed by decay products (daughters) of an out-of-equilibrium particle decay. While daughters mimic sterile neutrinos in N-eff and m(hdm)(eff), there are opportunities to assess this possibility in likelihood analyses. Connecting cosmological parameters and moments of momentum distribution functions, we show that also in the case of mass-degenerate daughters with indistinguishable main physical effects the mimicry breaks down when the next moment, the skewness, is considered. Predicted differences of order one in the root-mean-squares of absolute momenta are too small for current sensitivities.