  Cosmological observations such as structure formation, CMB, and cosmic
distance ladder set tight constraints to the amount and nature of dark matter
(DM). In particular structure formation strongly constraints not only the
amount of energy density, but also the time when DM became non-relativistic,
anr. Standard cold and thermic warm DM particles have a smooth transition from
being relativistic at high energies to a non-relativistic regime since the mass
of these particles is constant while the velocity redshifts with the expansion
of the universe. However, here we explore the possibility that the DM particle
acquires a non-perturbative mass at a phase transition scale and a scale factor
ac. This transition acquired a more fundamental meaning for the Bound Dark
Matter (BDM) model because they describe a particle getting its mass through a
non-perturbative process. These BDM particles may go from being relativistic to
non-relativistic at ac, which implies an abrupt transition of the velocity of
the particles vc at that time, affecting the equation of state and the
cosmological evolution. Here we study the cosmological impact of the values of
vc and the scale transition ac and they by reducing the free-streaming scale
and therefore the small scale structure. Using CMB Plank, Supernovae SNIa, and
BAO data, we constrain the valid region in the parameter space ac-vc putting
upper bounds to ac but not restricting vc. For instance, the transition must be
ac<$2.66\times10^{-6}$ for vc = 0. We also find that the free-streaming and the
Jeans mass of the dark matter particle is highly influenced by the velocity vc,
for example, a 3 keV WDM have a Jeans mass of Mfs=$1.97\times10^7$ Msun/h^3 but
an equivalent BDM with the same anr but an abrupt transition in the velocity,
vc~0 would have a Jeans mass of Mfs=$2.08x10^4$ Msun/h^3 which significantly
changes the large scale structure formation.
