  We study the ground state properties and the excitation spectrum of bosons
which, in addition to a short-range repulsive two body potential, interact
through the exchange of some dispersionless bosonic modes. The latter induces a
time dependent (retarded) boson-boson interaction which is attractive in the
static limit. Moreover the coupling with dispersionless modes introduces a
reference frame for the moving boson system and hence breaks the Galilean
invariance of this system. The ground state of such a system is depleted {\it
linearly} in the boson density due to the zero point fluctuations driven by the
retarded part of the interaction. Both quasiparticle (microscopic) and
compressional (macroscopic) sound velocities of the system are studied. The
microscopic sound velocity is calculated up the second order in the effective
two body interaction in a perturbative treatment, similar to that of Beliaev
for the dilute weakly interacting Bose gas. The hydrodynamic equations are used
to obtain the macroscopic sound velocity. We show that these velocities are
identical within our perturbative approach. We present analytical results for
them in terms of two dimensional parameters -- an effective interaction
strength and an adiabaticity parameter -- which characterize the system. We
find that due the presence of several competing effects, which determine the
speed of the sound of the system, three qualitatively different regimes can be
in principle realized in the parameter space and discuss them on physical
grounds.
