Cold keV dark matter from decays and scatterings

We explore ways of creating cold keV-scale dark matter by means of decays and scatterings. The main observation is that certain thermal freeze-in processes can lead to a cold dark matter distribution in regions with a small available phase space. In this way the free-streaming length of keV particles can be suppressed without decoupling them too much from the Standard Model. In all cases, dark matter needs to be produced together with a heavy particle that carries away most of the initial momentum. For decays, this simply requires an off-diagonal dark matter (DM) coupling to two heavy particles; for scatterings, the coupling of soft DM to two heavy particles needs to be diagonal, in particular in spin space. Decays can thus lead to cold light DM of any spin, while scatterings only work for bosons with specific couplings. We explore a number of simple models and also comment on the connection to the tentative 3.5 keV line.