Daughters mimic sterile neutrinos (almost!) perfectly

TL;DR

Cosmological observations can detect differences between sterile neutrinos and daughter particles from particle decay, but current sensitivities are insufficient to distinguish their subtle momentum distribution differences.

Contribution

The paper demonstrates that daughter particles from decay can mimic sterile neutrinos in cosmological data, but higher moments of their momentum distribution can break this degeneracy.

Findings

Daughters and sterile neutrinos produce similar effects in $N_{eff}$ and $m_{hdm}^eff$.

Skewness of momentum distribution can differentiate between the two scenarios.

Current sensitivities are too low to detect predicted differences.

Abstract

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.