The density response of a doped Mott‐Hubbard insulator is discussed starting from thet‐Jmodel in a slave boson 1/Nrepresentation. In leading orderO(1) the density fluctuation spectraN(q, &ohgr;) 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/Ncorrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resultingN(q, &ohgr;) 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 &khgr;J+ &dgr;trelated to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (&pgr;, 0) direction, describes the strong renormalization and anomalous damping of the highest bond‐stretching phonons in La2−xSrxCuO4. © 2003 American Institute of Physics