Sensitivity of inflationary predictions to pre-inflationary phases

How sensitive are the predictions of inflation to pre-inflationary conditions when the number of efolds of inflation is not too large? In an attempt to address this question, we consider a simple model where the inflationary era is preceded by an era dominated by a radiation fluid, which is coupled to the inflaton only gravitationally and which extends back to the Planck era. We show that there is a natural generalized Bunch-Davies vacuum state for perturbations to the coupled inflaton-gravity-fluid system at early times. With this choice of initial state the model predicts interesting deviations from the standard power spectrum of single field slow-roll inflation at large scales. However, the deviations are too small to be observable in near future CMB observations.