  Short baseline neutrino oscillation experiments have shown hints of the
existence of additional sterile neutrinos in the eV mass range. Such sterile
neutrinos are incompatible with cosmology because they suppress structure
formation unless they can be prevented from thermalising in the early Universe
or removed by subsequent decay or annihilation. Here we present a novel
scenario in which both sterile neutrinos and dark matter are coupled to a new,
light pseudoscalar. This can prevent thermalisation of sterile neutrinos and
make dark matter sufficiently self-interacting to have an impact on galactic
dynamics and possibly resolve some of the known problems with the standard cold
dark matter scenario. Even more importantly it leads to a strongly
self-interacting plasma of sterile neutrinos and pseudoscalars at late times
and provides an excellent fit to CMB data. The usual cosmological neutrino mass
problem is avoided by sterile neutrino annihilation to pseudoscalars. The
preferred value of $H_0$ is substantially higher than in standard $\Lambda$CDM
and in much better agreement with local measurements.
