Lower mass bounds on FIMP Dark Matter

Over the last decades, strong evidence for dark matter (DM) has been accumulated. However, its nature is still unknown in fundamental physics. A cold relic produced via thermal freeze-out has been the leading paradigm for a long period, both for its simplicity and versatility to include candidates offered by extensions of the Standard Model of particle physics. Despite a large experimental effort to detect these candidates, no conclusive evidence has been found yet. The outcome of these negative searches has been motivating the community to explore alternative paradigms to the freeze-out. One of these is the freeze-in scenario, first introduced by Hall et al. (2009), which shares the advantages of the freeze-out paradigm but in which DM is produced out of thermal equilibrium. In this work, after a review of the evidence of DM and the Boltzmann equation formalism, we present the main features of the freeze-in paradigm proving its efficiency in reproducing the relic density. Despite the usually smaller couplings between DM and visible matter in the freeze-in scenario, frozen-in DM candidates, called Feebly Interacting Particles (FIMPs), can have interesting observational features through which freeze-in models can be constrained. Among them, stringent bounds can come from structure formation data. In particular, too light FIMP DM is in tension with small-scales structures such as the Lyman-$\alpha$ forest. We develop a model independent procedure to constrain the parameter space of a FIMP model and to extract the value of the minimum DM mass allowed, which is of crucial importance in model building. The methodology is based on the comparison of the linear matter power spectrum, computed with the CLASS code, from the non-thermal FIMP phase-space distribution, with the limit power spectrum obtained from a Warm Dark Matter (WDM) model, found by M. Viel et al. (2017). To test our procedure and compare with the literature, we consider three simple scalar FIMP DM toy models involving renormalizable interactions with hypothetical scalars belonging to the thermal bath. These are benchmarks models in which DM production is dominated by decays and scatterings and can be used to draw general conclusions on FIMP DM produced via these mechanisms. The developed procedure can also be applied to concrete freeze-in models and frameworks in which the DM production occurs in modified cosmologies and can be generalized to include also additional external bounds on the linear matter power spectrum.