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We investigate the initial state of the inflationary universe. In our recentpublications, we showed that requesting the gauge invariance in the localobservable universe to the initial state guarantees the infrared (IR)regularity of loop corrections in a general single clock inflation. Followingthis study, in this paper, we show that choosing the Euclidean vacuum ensuresthe gauge invariance in the local universe and hence the IR regularity of loopcorrections. It has been suggested that loop corrections to inflationaryperturbations may yield the secular growth, which can lead to the break down ofthe perturbative analysis in an extremely long term inflation. The absence ofthe secular growth has been claimed by picking up only the IR contributions,which we think is incomplete because the non-IR modes which are comparable toor smaller than the Hubble scale potentially can contribute to the seculargrowth. We prove the absence of the secular growth without neglecting thesenon-IR modes to a certain order in the perturbative expansion. We also discusshow the regularity of the n-point functions for the genuinely gauge invariantvariable constrains the initial states of the inflationary universe. Theseresults apply in a fully general single field model of inflation.

progress of theoretical and experimental physics

Strong restriction on inflationary vacua from the local gauge invariance  II: Infrared regularity and absence of the secular growth in Euclidean vacuum