On Loops in Inflation II: IR Effects in Single Clock Inflation

TL;DR

This paper investigates the effects of mode coupling during single clock inflation, concluding that infrared modes do not produce significant physical effects, and clarifies the role of scale mapping and horizon crossing.

Contribution

It demonstrates the cancellation of infrared projection effects in physical observables and analyzes the stochastic nature of scale mapping corrections during inflation.

Findings

Infrared modes do not affect physical observables in inflation.

The scale mapping correction is enhanced by the number of e-folds, N_e.

The variance of the stochastic correction is not amplified by N_e.

Abstract

In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing fluctuations as a function of physically measurable scales. Modes on scales smaller than the one of interest change the mapping between horizon crossing time and scale. The correction to the mapping computed in the absence of fluctuations is enhanced by a factor N_e, the number of e-folds of inflation between horizon crossing and reheating. The new mapping is stochastic in nature but its variance is not enhanced by N_e.