BDM Dark Matter: CDM with a core profile and a free streaming scale

We present a new dark matter model BDM which is an hybrid between hot dark matter HDM and cold dark matter CDM, in which the BDM particles behave as HDM above the energy scale E_c and as CDM below this scale. Evolution of structure formation is similar to that of CDM model but BDM predicts a nonvanishing free streaming l_fs scale and a inner galaxy core radius r_core, both quantities determined in terms of a single parameter E_c, which corresponds to the phase transition energy scale of the subjacent elementary particle model. For energies above E_c or for a scale factor a smaller then a_c, with a<a_c<a_{eq}, the particles are massless and rho redshifts as radiation. However, once the energy becomes E\leq E_c or a>a_c then the BDM particles acquire a large mass through a non perturbative mechanism, as baryons do, and rho redshifts as matter with the particles having a vanishing velocity. Typical energies are E_c=O(10-100) eV giving a l_fs \propto E_c^{-4/3}\lesssim Mpc and m_fs\propto E_c^{-4}\lesssim 10^9 M\odot. A l_fs\neq 0, r_core\neq 0 help to resolve some of the shortcomings of CDM such as overabundance substructure in CDM halos and numerical fit to rotation curves in dwarf spheroidal and LSB galaxies. Finally, our BDM model and the phase transition scale E_c can be derived from particle physics.