Minimal Theoretical Uncertainties in Inflationary Predictions

TL;DR

The paper identifies a fundamental, minimal theoretical uncertainty in inflationary predictions that arises from vacuum ambiguity: BD and adiabatic vacua do not uniquely specify the initial quantum state for curvature perturbations when inflation has finite duration, even in the absence of trans-Planckian effects. The authors quantify the resulting uncertainties for slow-roll and general FRW spacetimes, showing them to be generically small, and provide explicit scaling forms for the BD and adiabatic cases. In the BD case, the curvature perturbation spectrum uncertainty scales roughly as $\delta{\cal P}_{\cal R}(k)/{\cal P}_{\cal R}(k) \sim O(|B_k|)$ with $|B_k| \sim e^{-(N_0-N_k)}$, becoming negligible if the inflationary period far exceeds the horizon-exit time of the modes of interest. In the adiabatic vacuum, nonperturbative effects can yield even more suppressed uncertainties (e.g., $|B_k|$ obeying double-exponential forms), though in quasi-de Sitter slow-roll spacetimes the overall impact remains minimal. Overall, this minimal vacuum-induced uncertainty sets a baseline for inflationary calculations and helps distinguish genuine new-physics signals from inherent theoretical ambiguity.

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.