Influence on Observation from IR Divergence during Inflation. I: Single Field Inflation

Abstract

A naive computation of the correlation functions of fluctuations generated during inflation suffers from logarithmic divergences in the infrared (IR) limit. In this paper, we propose one way to solve this IR divergence problem in the single-field inflation model. The key observation is that the variables that are commonly used in describing fluctuations are influenced by what we cannot observe. Introducing a new perturbation variable which mimics what we actually observe, we propose a new prescription to solve the time evolution of perturbation in which this leakage of information from the unobservable region of the universe is shut off. We give a proof that IR divergences are absent as long as we follow this new scheme. We also show that the secular growth of the amplitude of perturbation is also suppressed, at least, unless very higher order perturbation is discussed.