On Squeezed Limits in Single-Field Inflation - Part I

TL;DR

This paper investigates the squeezed limit of the bispectrum in single-field inflation, showing that potential violations of consistency conditions are undetectably small in known models and under typical initial states.

Contribution

It demonstrates that in the regime of theoretical control, excited initial states do not produce detectable signals in the squeezed limit of the bispectrum in single-field inflation.

Findings

Violations of consistency conditions are undetectably small in known models.

Excited states related to the Bunch-Davies state produce negligible signals.

Slow-roll conditions remain valid for small-energy excited states.

Abstract

The n-point correlation functions in single-field inflation obey a set of consistency conditions in the exact squeezed limit which are not present in multi-field models, and thus are powerful tools to distinguish between the two. However, these consistency conditions may be violated for a finite range of scales in single-field models, for example by departures from the Bunch-Davies state. These it excited states may be the consequence of interactions during inflation, or may be a remnant of the era that preceded inflation. In this paper we analyze the bispectrum, and show that in the regime of theoretical control the resulting signal in the squeezed limit remains undetectably small in all known models which continuously excite the state. We also show that the signal remains undetectably small if the initial state is related to the Bunch-Davies state by a Bogoliubov transformation and the energy density in the state is small enough so that the usual slow-roll conditions are obeyed. Bogoliubov states that lead to violations of the slow-roll conditions, as well as more general excited states, require more careful treatment and will be discussed in a separate publication.