Daughters mimic sterile neutrinos (almost!) perfectly
  Since only recently, cosmological observations are sensitive to hot dark
matter (HDM) admixtures with sub-eV mass, $m_\text{hdm}^\text{eff}$ < eV, that
are not fully-thermalised, $N_\text{eff}$ < 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 $N_\text{eff}$ and
$m_\text{hdm}^\text{eff}$, 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.
