Influence of gauge artifact on adiabatic and entropy perturbations during inflation

Abstract

In recent publications we proposed one way to calculate gauge-invariant variables in the local observable universe, which is limited to a portion of the whole universe. To provide a theoretical prediction of the observable fluctuations, we need to preserve the gauge-invariance in the local universe, which is referred to the genuine gauge-invariance. The importance of the genuine gauge-invariance is highlighted in the study of primordial fluctuations in the infrared (IR) limit. The stability against IR loop corrections to primordial fluctuations is guaranteed in requesting the genuine gauge-invariance. The genuine gauge-invariance also gives the impact on the detectable fluctuations. We showed that at observable scales the bi-spectrum calculated in the conventional perturbation theory vanishes in the squeezed limit, if we request the genuine gauge invariance. This indicates that the conventional bi-spectrum is, in this limit, dominated by a gauge artifact, which cannot be observed. These studies have been elaborated in single-field models of inflation. In this paper we generalize our argument to multi-field models of inflation, where, in addition to the adiabatic field, the entropy field can participate in the generation of primordial fluctuations. We will find that the entropy field can generate the observable fluctuations, which cannot be eliminated by gauge transformations in the local universe.