Extra relativistic degrees of freedom without extra particles using Planck data

A recent number of analysis of cosmological data have shown indications for the presence of extra radiation beyond the standard model at equality and nucleosynthesis epoch, which has been usually interpreted as an effective number of neutrinos, Neff > 3.046. In this work we establish the theoretical basis for a particle physics-motivated model (Bound Dark Matter, BDM) which explain the need of extra radiation. The BDM model describes dark matter particles which are relativistic at a scale below a < ac, these particles acquire mass with an initial velocity, vc, at scales a > ac due to non-perturbative methods, as protons and neutrons do, this process is described by a time dependent equation of state, w_bdm(a). Owing to this behavior the amount of extra radiation change as a function of the scale factor, this entail that the extra relativistic degrees of freedom Nex may also vary as a function of the scale factor. This is favored by data at CMB and BBN epochs. We compute the range of values of the BDM model parameters, xc = ac*vc, that explain the values obtained for the 4He at BBN and Neff at equality. Combining different analysis we compute the value xc = 4.13x10^{-5} and vc = 0.37. We conclude that we can account for the apparent extra neutrino degrees of freedom Nex using a phase transition in the dark matter with a time dependent equation of state with no need for introducing extra relativistic particles.