Dark energy and limit of existence of self-gravitating dark matter clusters: Fermions and bosons

The stability of any self-gravitating cluster of matter is affected by the repulsive effect of the so-called dark energy. Using a simple method we estimate the limit of existence of Newtonian clusters formed by pure fermion or boson populations in their ground state. These clusters simulate lumps of dark matter. As the length scale of the clusters is limited by the effect of dark energy, this implies a lower bound for their mass. From these bounds for the clusters one can infer constraints for the mass of the underlying constituent dark matter particle. The computations are carried out comparing two characteristic length scales which provide an order of magnitude for this problem. The repulsive effect of dark energy is implemented by using an up-to-date value of the cosmological constant. For both fermions and bosons, the condition of existence is expressed in a similar way and a significant common mass scale is identified.