  A number of experimental anomalies involving neutrinos hint towards the
existence of at least an extra (a very light) sterile neutrino. However, such a
species, appreciably mixing with the active neutrinos, is disfavored by
different cosmological observations like Big Bang Nucleosynthesis (BBN), Cosmic
Microwave Background (CMB) and Large Scale Structure (LSS). Recently, it was
shown that the presence of additional interactions in the sterile neutrino
sector via light bosonic mediators can make the scenario cosmologically viable
by suppressing the production of the sterile neutrinos from active neutrinos
via matter-like effect caused by the mediator. This mechanism works assuming
the initial population of this sterile sector to be negligible with respect to
that of the Standard Model (SM) particles, before the production from active
neutrinos. However, there is fair chance that such bosonic mediators may couple
to the inflaton and can be copiously produced during (p)reheating epoch.
Consequently, they may ruin this assumption of initial small density of the
sterile sector. In this article we, starting from inflation, investigate the
production of such a sterile sector during (p)reheating in a large field
inflationary scenario and identify the parameter region that allows for a
viable early Universe cosmology.
