Arbitrariness of inflationary fluctuation spectra

We find that the simplest model of inflation, a single scalar field undergoing slow roll, is consistent with nearly arbitrary fluctuation power spectra, each corresponding to a unique family of potentials which we determine. Deviations from a Zel'dovich spectrum become increasingly dramatic in the limit that the slow-roll approximation breaks down. Examples are given. Possible features in the power spectrum could reconcile galaxy formation theories with observations of large-scale structure. We further derive new constraints on the reheating temperature.