Sterile neutrinos with eV masses in cosmology -- how disfavoured
  exactly?
  We study cosmological models that contain sterile neutrinos with eV-range
masses as suggested by reactor and short-baseline oscillation data. We confront
these models with both precision cosmological data (probing the CMB decoupling
epoch) and light-element abundances (probing the BBN epoch). In the minimal
LambdaCDM model, such sterile neutrinos are strongly disfavoured by current
data because they contribute too much hot dark matter. However, if the
cosmological framework is extended to include also additional relativistic
degrees of freedom -- beyond the three standard neutrinos and the putative
sterile neutrinos, then the hot dark matter constraint on the sterile states is
considerably relaxed. A further improvement is achieved by allowing a dark
energy equation of state parameter w<-1. While BBN strongly disfavours extra
radiation beyond the assumed eV-mass sterile neutrino, this constraint can be
circumvented by a small nu_e degeneracy. Any model containing eV-mass sterile
neutrinos implies also strong modifications of other cosmological parameters.
Notably, the inferred cold dark matter density can shift up by 20 to 75%
relative to the standard LambdaCDM value.
