Cosmological bounds on heavy neutral leptons with dark decay channels

Heavy neutral leptons (HNLs) are well-motivated new physics candidates. The mixing of sub-GeV HNLs with active neutrinos is severely constrained by cosmology. In particular, the success of big bang nucleosynthesis (BBN) requires the HNL lifetime to be shorter than about 0.02 sec if they were in thermal equilibrium, thus excluding a wide range of mixing angles accessible to terrestrial experiments. In order to justify the laboratory searches in this cosmologically forbidden region, it is often argued that adding new dark sector decay modes of HNLs can evade the stringent BBN constraint. Here we rule out this possibility and show that, contrary to the naive expectation, HNLs with significant dark decay modes actually lead to stronger cosmological bounds. This is mainly because of the increase in the extra radiation energy density in the Universe around the BBN epoch, which causes observable effects in the primordial helium fraction and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Δ</a:mi> <a:msub> <a:mi>N</a:mi> <a:mi>eff</a:mi> </a:msub> </a:math> . Our result has major implications for laboratory searches of HNLs.