Cosmological dependence of non-resonantly produced sterile neutrinos

We discuss how a laboratory detection of a sterile neutrino not only would constitute a fundamental discovery of a new particle, but could also provide an indication of the evolution of the Universe before Big-Bang Nucleosynthesis (BBN), a fundamental discovery in cosmology. These "visible" sterile neutrinos could be detected in experiments such as KATRIN/TRISTAN and HUNTER in the keV mass range and PTOLEMY, KATRIN and reactor neutrino experiments in the eV mass range. Standard assumptions are usually made to compute the relic abundance and momentum distribution of particles produced before the temperature of the Universe was 5 MeV, an epoch from which there are no observed remnants thus far. However, non-standard pre-BBN cosmologies based on other assumptions that are equally in agreement with all existing data can arise in some theoretical models. We revisit the production of 0.01 eV to 1 MeV sterile neutrinos via non-resonant active-sterile flavor oscillations in several pre-BBN cosmologies. We give general equations for models in which the expansion of the Universe is parametrized by its amplitude and temperature power and where entropy is conserved, which include kination and scalar tensor models as special cases.