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Effects of kination and scalar-tensor cosmologies on sterile neutrinos

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.