Thermal production of cold "hot dark matter" around eV

A very simple production mechanism of feebly interacting dark matter (DM) that rarely annihilates is thermal production, which predicts the DM mass around eV. This has been widely known as the hot DM scenario. Despite there are several observational hints from background lights suggesting a DM in this mass range, the hot DM scenario has been considered strongly in tension with the structure formation of our Universe because the free-streaming length of the DM produced from thermal reactions was thought to be too long. In this paper, I show that the previous conclusions are not always true depending on the reaction for bosonic DM because of the Bose-enhanced reaction at very low momentum. By using the simple $1\leftrightarrow 2$ decay/inverse decay process to produce the DM, I demonstrate that the eV range bosonic DM can be thermally produced $coldly$ from a hot plasma by performing a model-independent analysis applicable to axion, hidden photon, and other bosonic DM candidates. Therefore, the bosonic DM in the eV mass range may still be special and theoretically well-motivated.