Minimal theoretical uncertainties in inflationary predictions

Abstract

During inflation, primordial energy density fluctuations are createdfrom approximate de Sitter vacuum quantum fluctuations redshifted outof the horizon, after which they are frozen as perturbations in thebackground curvature. In this paper we demonstrate that there existsan intrinsic theoretical uncertainty in the inflationary predictionsfor the curvature perturbations, due to the failure of the well knownprescriptions to specify the vacuum uniquely. Specifically, we showthat the two often used prescriptions for defining the initial vacuumstate—the Bunch–Davies prescription and the adiabatic vacuumprescription (even if the adiabaticity order to which the vacuum isspecified is infinity)—fail to specify the vacuum uniquely ingeneric inflationary spacetimes in which the total duration ofinflation is finite. This conclusion holds despite the absence of anytrans-Planckian effects or effective field theory cutoff relatedeffects. We quantify the uncertainty which is applicable to slow rollinflationary scenarios as well as for general FRW spacetimes and findthat the uncertainty is generically small. This uncertaintyshould be treated as a minimal uncertainty that underlies allcurvature perturbation calculations.