The ground state properties and the excitation spectrum  of a system of interacting bosons which  moreover are coupled to the local vibrational modes of the lattice are studied.
The lowest order approximation to the problem  is obtained within a Bogoliubov scheme and the generalized Beliaev-Popov formalism is employed to treat the fluctuation effects as well as the retarded nature of phonon mediated interaction. It is shown,  that two competing effects determine the collective sound wave-like  mode with sound velocity $v$, arising from gauge
symmetry breaking:
i) The sound velocity $v_0$ (corresponding to a weakly interacting Bose system on a rigid lattice) in the lowest order approximation is reduced due to reduction of the repulsive boson-boson interaction, arising from the attractive part of phonon mediated interaction in the static limit.
ii) the second order correction to the sound velocity is enhanced  as compared to the one of bosons on a rigid lattice when the the boson-phonon interaction is switched on due to the retarded nature of phonon mediated interaction. The macroscopic sound velocity of the system is obtained 
from the hydrodynamic equations and shown to be identical to microscopic one.