Displaced vertices at colliders, arising from the production and decay of long-lived particles, probe dark matter candidates produced via freeze-in. If one assumes a standard cosmological history, these decays happen inside the detector only if the dark matter is very light because of the relic density constraint. Here, we argue how displaced events could very well point to freeze-in within a non-standard early universe history. Focusing on the cosmology of inflationary reheating, we explore the interplay between the reheating temperature and collider signatures for minimal freeze-in scenarios. Observing displaced events at the LHC would allow to set an upper bound on the reheating temperature and, in general, to gather indirect information on the early history of the universe.

In this paper we study a leptophilic dark matter scenario involving feeble dark matter coupling to the Standard Model (SM) and compressed dark matter-mediator mass spectrum. We consider a simplified model where the SM is extended with one Majorana fermion, the dark matter, and one charged scalar, the mediator, coupling to the SM leptons through a Yukawa interaction. We first discuss the dependence of the dark matter relic abundance on the Yukawa coupling going continuously from freeze-in to freeze-out with an intermediate stage of conversion driven freeze-out. Focusing on the latter, we then exploit the macroscopic decay length of the charged scalar to study the resulting long-lived-particle signatures at collider and to explore the experimental reach on the viable portion of the parameter space. e.g. [1][2][3][4]. In some parts of this parameter space, the DM happens to be very feebly coupled to the SM, i.e. with couplings much more suppressed than for the WIMP case.We focus on this feeble interaction window for scenarios involving a small mass splitting between the dark matter and the mediator connecting DM to the SM. We will study in details the mechanism of dark matter production in the early universe, from freezein to freeze-out. In particular, we will mainly focus on the intermediate stage of DM coannihilation freeze-out happening out of chemical equilibrium (CE) with the SM plasma, also called conversion driven freeze-out. Such a scenario has already been pointed out in [3] and mainly studied for dark matter coupling to quarks [3,5,6]. Here instead we focus on the case of a leptophilic dark matter model. Conversion processes between the mediator and the dark matter will play a central role in defining the evolution of the DM abundance and they will have to be taken into account in the study of the DM/mediator Boltzmann equations. In passing, we will also emphasize the fact that, within the freeze-in framework, mediator scatterings (as opposed to decay) can play a leading role in determining the DM relic density. Finally, we will identify the viable parameter space for conversion driven freeze-out so as to further study the experimental constraints on this class of models.The feeble coupling of the DM to the mediator allows for a macroscopic decay length of the mediator that can be observed at colliders through e.g. charged and/or disappearing tracks. These are typical features of DM scenarios in which the DM abundance results from the freeze-in [4] and conversion driven freeze-out [3]. These production mechanisms can lead to distinctive and challenging signatures at colliders, including long lived charged particles and very soft signatures. In the freeze-in case, the DM coupling is so suppressed that the mediator mainly decays outside the detector giving rise to charged tracks. For conversion driven freeze-out, the slightly larger couplings involved can also give rise to disappearing tracks. The LHC community has already provided a strong effort in the study of final state signatures which arise from DM mo...