The robustness of inflation to changes in super-Planck-scale physics

We calculate the spectrum of density fluctuations in models of inflation ba sed on a weakly self-coupled scalar matter field minimally coupled to gravi ty, and specifically investigate the dependence of the predictions on modif ications of the physics on length scales smaller than the Planck length. Th ese modifications are encoded in terms of modified dispersion relations. Wh ereas far some classes of dispersion relations the predictions are unchange d compared to the usual ones which are based on a linear dispersion relatio n, for other classes important differences are obtained, involving tilted s pectra, spectra with exponential factors and with oscillations. This is the case when the dispersion relation becomes complex. We conclude that the pr edictions of inflationary cosmology in these models are not robust against changes in the super-Planck-scale physics.