Natural Selection of Inflationary Vacuum Required by Infra-Red Regularity and Gauge-Invariance

Abstract

It has been an issue of debate whether the inflationary infrared(IR) divergences are physical or not. Our claim is that, at least, in single-field models, the answer is "No," and that the spurious IR divergence is originating from the careless treatment of the gauge modes. In our previous work we have explicitly shown that the IR divergence is absent in the genuine gauge-invariant quantity at the leading order in the slow-roll approximation. We extend our argument to include higher-order slow-roll corrections and the contributions from the gravitational waves. The key issue is to assure the gauge invariance in the choice of the initial vacuum, which is a new concept that has not been considered in conventional calculations.