Minimal Theoretical Uncertainties in Inflationary Predictions

Abstract

During inflation, primordial energy density fluctuations are created from approximate de Sitter vacuum quantum fluctuations redshifted out of the horizon after which they are frozen as perturbations in the background curvature. In this paper we demonstrate that there exists an intrinsic theoretical uncertainty in the inflationary predictions for the curvature perturbations due to the failure of the well known prescriptions to specify the vacuum uniquely. Specifically, we show that the two often used prescriptions for defining the initial vacuum state -- the Bunch-Davies prescription and the adiabatic vacuum prescription (even if the adiabaticity order to which the vacuum is specified is infinity) -- fail to specify the vacuum uniquely in generic inflationary spacetimes in which the total duration of inflation is finite. This conclusion holds despite the absence of any trans-Planckian effects or effective field theory cutoff related effects. We quantify the uncertainty which is applicable to slow roll inflationary scenarios as well as for general FRW spacetimes and find that the uncertainty is generically small. This uncertainty should be treated as a minimal uncertainty that underlies all curvature perturbation calculations.