Influence on observation from IR divergence during inflation -- Single field inflation --

TL;DR

The paper tackles IR divergences in nonlinear perturbations during single-field inflation by arguing that observable fluctuations must be described within a causally connected region using a local gauge. It introduces a new perturbation variable and a windowed, locally fixed gauge that shuts off information leakage from unobservable regions, and develops an iterative scheme to compute higher-order terms via retarded dynamics. The authors prove IR regularity for all $n$-point functions under this prescription and show that secular growth is suppressed up to high order, with potential initial-time dependence emerging only at very high order through early-epoch effects. The work provides a physically motivated framework for finite, observable predictions in single-field inflation and discusses extensions to multi-field cases and connections to stochastic decoherence methods for addressing residual IR issues in more complex models.

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.

Figures (4)

• Figure 1: One-loop diagram having one four-point interaction vertex for the two-point correlation function.
• Figure 2: Diagrammatic expression for the Heisenberg field expanded in terms of the interaction picture fields when only the three point interaction vertex is present. Here the Heisenberg field, the interaction picture field, and the retarded Green function are represented by a thick line, a thin line and a thin line with the index "$R$", respectively.
• Figure 3: Summary of the iteration scheme to obtain higher order perturbation $\tilde{\varphi}_n$.
• Figure 4: The dark grey region represents the region (i). The light grey region represents the region (ii). These two regions are divided by the solid curve which shows the scale of the causally connected region, i.e., $k = L_t^{-1}$. The dashed line is the horizon scale, i.e., $k = a(t) H(t)$, which corresponds to the effective UV cutoff scale.