  The role of the electron-phonon interaction in the Holstein-Hubbard model is
investigated in the metallic phase close to the Mott transition and in the
insulating Mott phase. The model is studied by means of a variational slave
boson technique. At half-filling, mean-field static quantities are in good
agreement with the results obtained by numerical techniques. By taking into
account gaussian fluctuations, an analytic expression of the spectral density
is derived in the Mott insulating phase showing that an increase of the
electron-phonon coupling leads to a sensitive reduction of the Mott gap through
a reduced effective repulsion. The relation of the results with recent
experimental observations in strongly correlated systems is discussed.
