Vacuum Choices and the Predictions of Inflation
C. Armendariz-Picon, Eugene A. Lim
TL;DR
This work addresses vacuum ambiguity during inflation in a universe with a short-distance cutoff by introducing a phenomenological two-parameter vacuum description with complex parameters $X$ and $Y$. Initial conditions for each mode are imposed at a finite time characterized by the scale $\Lambda^{-1}$ (or equivalently at a fixed $H=\Lambda$), and the resulting imprint on the curvature power spectrum is derived; corrections are oscillatory with amplitude scaling as $H/\Lambda$ for cutoff-crossing initialization and can be highly suppressed for equal-$H$ initialization. By analyzing gravitational particle production, the authors obtain observational bounds that constrain $|X|$ (e.g., $|X| \lesssim 1.1$ for $\Lambda = M_{Pl}$), with the Danielsson prescription remaining viable. The main conclusion is that inflationary predictions are robust at zeroth order, while first-order vacuum effects are Planck-suppressed and depend on the chosen initialization scheme and vacuum prescription, offering a practical route to test vacuum choices via observations.
Abstract
In the presence of a short-distance cutoff, the choice of a vacuum state in an inflating, non-de Sitter universe is unavoidably ambiguous. The ambiguity is related to the time at which initial conditions for the mode functions are specified and to the way the expansion of the universe affects those initial conditions. In this paper we study the imprint of these uncertainties on the predictions of inflation. We parametrize the most general set of possible vacuum initial conditions by two phenomenological variables. We find that the generated power spectrum receives oscillatory corrections whose amplitude is proportional to the Hubble parameter over the cutoff scale. In order to further constrain the phenomenological parameters that characterize the vacuum definition, we study gravitational particle production during different cosmological epochs.