Active-sterile neutrino oscillations in the early Universe with full
  collision terms
  Sterile neutrinos are thermalised in the early Universe via oscillations with
the active neutrinos for certain mixing parameters. The most detailed
calculation of this thermalisation process involves the solution of the
momentum-dependent quantum kinetic equations, which track the evolution of the
neutrino phase space distributions. Until now the collision terms in the
quantum kinetic equations have always been approximated using equilibrium
distributions, but this approximation has never been checked numerically. In
this work we revisit the sterile neutrino thermalisation calculation using the
full collision term, and compare the results with various existing
approximations in the literature. We find a better agreement than would naively
be expected, but also identify some issues with these approximations that have
not been appreciated previously. These include an unphysical production of
neutrinos via scattering and the importance of redistributing momentum through
scattering, as well as details of Pauli blocking. Finally, we devise a new
approximation scheme, which improves upon some of the shortcomings of previous
schemes.
