The mass spectrum of collapsed objects in the universe depends on the details of the microphysical cooling and feedback mechanisms involved in the collapse. In the first part of the talk, I explicate this connection in the context of the formation of the first stars in mini-haloes cooled by molecular hydrogen. In the second part, I discuss the cooling of hydrogen-like "atomic dark matter" clouds. The collapse of dark gas clouds cooled by dark atoms and dark molecules can lead to the formation of compact objects in mass ranges forbidden by ordinary stellar astrophysics, whose mergers could be detectable by current gravitational wave observatories.