On the initial condition of inflationary fluctuations

TL;DR

This paper verifies the assumptions of Bunch-Davies initial conditions in inflationary fluctuations by calculating loop corrections, showing they suppress non-BD contributions and regularize non-Gaussianities.

Contribution

The authors develop a new loop chain diagram resummation technique to explicitly verify and analyze the initial conditions of inflationary fluctuations.

Findings

Loop corrections suppress non-BD coefficients.

Resummation leads to exponential suppression factors.

Non-Gaussianities are regularized in the folded limit.

Abstract

It is usually assumed that the inflationary fluctuations start from the Bunch-Davies (BD) vacuum and the $i\varepsilon$ prescription is used when interactions are calculated. We show that those assumptions can be verified explicitly by calculating the loop corrections to the inflationary two-point and three-point correlation functions. Those loop corrections can be resumed to exponential factors, which suppress non-BD coefficients and behave as the $i\varepsilon$ factor for the case of the BD initial condition. A new technique of loop chain diagram resummation is developed for this purpose. For the non-BD initial conditions which is setup at finite time and has not fully decayed, explicit correction to the two-point and three-point correlation functions are calculated. Especially, non-Gaussianity in the folded limit is regularized due to the interactions.