  The LSND and MiniBooNE results as well as the reactor and Gallium anomalies
seem to indicate the presence of a sterile neutrino with a mass of $\sim 1$ eV
mixed with active neutrinos. Such sterile neutrino can be produced in the early
universe before the neutrino decoupling, leading to a contribution to the
effective number of neutrinos ($N_{eff}$) as well as to a contribution to the
sum of neutrino masses which are in tension with cosmological observations. We
propose a scenario to relax this tension by a Yukawa coupling of the sterile
neutrinos to ultra-light scalar particles which contribute to the dark matter
in the background. The coupling induces an effective mass for $\nu_s$ which
prevents its production in the early universe. We discuss the implications for
the upcoming KATRIN experiment and future relic neutrino search experiments
such as PTOLEMY. We also briefly comment on certain non-renormalizable forms of
interaction between $\nu_s$ and the scalar and their consequences for the
$\nu_s$ production in the early universe.
