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

TL;DR

This paper tackles IR divergences in nonlinear inflationary perturbations within multi-field models by redefining observables as local perturbations—deviations from local averages—and incorporating a decoherence-aware projection that selects a single decohered world. It develops a formal framework using local gauge fixing, tree-graph expansions with a causally regular $G_{\rm R}$, and a sequence of basis changes to isolate IR-unsafe sectors, proving IR finiteness of the observable $n$-point functions for finite-duration interactions. The key contributions are the IRVSF-based inductive proof, the two Bogoliubov transformations to confine IR issues to a squeezed $p=0$ sector, and the introduction of a Gaussian projection ${\cal P}$ with width $\sigma$ satisfying $H/M_{\rm pl} \ll \sigma \ll 1$ to model decoherence effects. The results support reliable predictions for non-Gaussian observables in multi-field inflation and offer a pathway to connect with stochastic approaches, while highlighting ongoing questions about the precise physical interpretation of the projected observables.

Abstract

We propose one way to regularize the fluctuations generated during inflation, whose infrared (IR) corrections diverge logarithmically. In the case of a single field inflation model, recently, we proposed one solution to the IR divergence problem. There, we introduced new perturbative variables which better mimic actual observable fluctuations, and proved the regularity of correlation functions with respect to these variables. In this paper, we extend our previous discussions to a multi field inflation model. We show that, as long as we consider the case that the non-linear interaction acts for a finite duration, observable fluctuations are free from IR divergences in the multi field model, too. In contrast to the single field model, to discuss observables, we need to take into account the effects of quantum decoherence which pick up a unique history of the universe from various possibilities contained in initial quantum state set naturally in the early stage of the universe.

Figures (1)

• Figure 1: Two Bogoliubov transformations