The Robustness of Inflation to Changes in Super-Planck-Scale Physics

4 pages, 1 figure. One important correction in the Corley/Jacobson case with b_m>0 and some misprints corrected.We calculate the spectrum of density fluctuations in models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, and specifically investigate the dependence of the predictions on modifications of the physics on length scales smaller than the Planck length. These modifications are encoded in terms of modified dispersion relations. Whereas for some classes of dispersion relations the predictions are unchanged compared to the usual ones which are based on a linear dispersion relation, for other classes important differences are obtained, involving tilted spectra, spectra with exponential factors and with oscillations. We conclude that the predictions of inflationary cosmology in these models are not robust against changes in the super-Planck-scale physics