  We study the effects of kination and scalar-tensor pre-Big Bang
Nucleosynthesis cosmologies on the non-resonant production of sterile
neutrinos. We show that if the peak of the production rate of sterile neutrinos
occurs during the non-standard cosmological phase, the relic number density of
sterile neutrinos could be reduced with respect to the number expected in the
standard cosmology. Consequently, current bounds on active-sterile neutrino
mixing derived from the relic energy density of sterile neutrinos could be
greatly relaxed. In particular, we show that the sterile neutrinos which could
explain the anomalies found in short-baseline neutrino experiments are
compatible with recent joint Planck upper limits on their contribution to the
energy density of the Universe in a scalar-tensor or a low-reheating
temperature pre-Big Bang Nucleosynthesis cosmology.
