Classical and quantum evolution of inflationary fluctuations

TL;DR

This paper compares quantum and classical calculations of inflationary perturbations, showing they diverge over time if interactions are relevant, with implications for primordial fluctuation statistics.

Contribution

It demonstrates that classical and quantum correlation functions of inflationary fluctuations differ exponentially over time when interactions are considered.

Findings

Quantum and classical correlations agree initially but diverge exponentially with e-folds.

Differences are illustrated using the bispectrum and tensor power spectrum.

Classical evolution from finite time does not produce poles in the scalar bispectrum.

Abstract

We compare the correlation functions of inflationary perturbations computed either with quantum or classical dynamics. Even if they are enforced to agree at a specific time during inflation, classical and quantum correlations will differ at the end of inflation, provided that interactions are relevant. The difference between the results of the classical and quantum computations is exponentially sensitive to the number of e-folds elapsed from the time of agreement. We illustrate this finding with the tree-level bispectrum of the primordial curvature fluctuation and the one-loop power spectrum of tensor modes. We also show that classical evolution from a finite time does not imply the appearance of poles in the scalar bispectrum.