Trans-Planckian dispersion and scale invariance of inflationary perturbations

We question the insensitivity of the predictions of inflationary models with respect to modifications of Planck energy physics. The modification we consider consists in replacing the usual dispersion relation by nonlinear ones. This way of addressing the problem has recently received attention and contradictory results were found. Our main result is to show that the adiabaticity of the mode propagation and the separation of two scales of interest, the Planck scale and the cosmological horizon scale, are sufficient conditions for the predictions to be unchanged. We then show that almost all models satisfy the first condition when the second is met. Therefore the introduction of a nonlinear dispersion is unlikely to have any discernable effects on the power spectrum of cosmological perturbations.