  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.
