Thermalisation of light sterile neutrinos in the early universe
  Recent cosmological data favour additional relativistic degrees of freedom
beyond the three active neutrinos and photons, often referred to as 'dark'
radiation. Light sterile neutrinos is one of the prime candidates for such
additional radiation. However, constraints on sterile neutrinos based on the
current cosmological data have been derived using simplified assumptions about
thermalisation of the sterile neutrino at the Big Bang Nucleosynthesis (BBN)
epoch. These assumptions are not necessarily justified and here we solve the
full quantum kinetic equations in the (1 active + 1 sterile) scenario and
derive the number of thermalised species just before BBN begins (T~1MeV) for
null (L=0) and large (L=0.01) initial lepton asymmetry and for a range of
possible mass-mixing parameters. We find that the full thermalisation
assumption during the BBN epoch is justified for initial small lepton asymmetry
only. Partial or null thermalisation occurs when the initial lepton asymmetry
is large.
