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We perform a detailed and illustrative study of the production of keV sterileneutrino Dark Matter (DM) by decays of singlet scalars in the early Universe.In the current study we focus on providing a clear and general overview of thisproduction mechanism. For the first time we study all regimes possible on thelevel of momentum distribution functions, which we obtain by solving a systemof Boltzmann equations. These quantities contain the full information about theproduction process, which allows us to not only track the evolution of the DMgeneration but to also take into account all bounds related to the spectrum,such as constraints from structure formation or from avoiding too much darkradiation. In particular we show that this simple production mechanism can,depending on the regime, lead to strongly non-thermal DM spectra which may evenfeature more than one peak in the momentum distribution. These cases could haveparticularly interesting consequences for cosmological structure formation, astheir analysis requires more refined tools than the simplistic estimate usingthe free-streaming horizon. Here we present the mechanism including allconcepts and subtleties involved, for now using the assumption that theeffective number of relativistic degrees of freedom is constant during DMproduction, which is applicable in a significant fraction of the parameterspace. This allows us to derive analytical results to back up our detailednumerical computations, thus leading to the most comprehensive picture of keVsterile neutrino DM production by singlet scalar decays that exists up to now.

keV Sterile Neutrino Dark Matter from Singlet Scalar Decays: Basic Concepts and Subtle Features