  The density response of a doped Mott-Hubbard insulator is discussed starting
from the t-J model in a slave boson 1/N representation. In leading order O(1)
the density fluctuation spectra $N({\bf q},\omega)$ are determined by an
undamped collective mode at large momentum transfer, in striking disagreement
with results obtained by exact diagonalization, which reveal a very broad
dispersive peak, reminescent of strong spin-charge coupling. The 1/N
corrections introduce the polaron character of the bosonic holes moving in a
uniform RVB background. The resulting $N({\bf q},\omega)$ captures all features
observed in diagonalization studies, fulfills the appropriate sum rules, and
apart from the broadening of the collective mode shows a new low energy feature
at the energy $\chi J+\delta t$ related to the polaron motion in the spinon
background. It is further shown that the low energy structure, which is
particularly pronounced in $(\pi,0)$ direction, describes the strong
renormalization and anomalous damping of the highest bond-stretching phonons in
La$_{2-x}$Sr$_x$CuO$_4$.
