Quantitative classicality in cosmological interactions during inflation

TL;DR

This paper investigates when inflationary cosmological perturbations can be accurately described by classical physics rather than quantum mechanics, providing criteria for the validity of classical approximations in early universe models.

Contribution

It introduces a quantitative framework to determine scales and times where classical evolution suffices for inflationary perturbations, based on the analysis of quantum interactions and the Keldysh formalism.

Findings

Squeezed limit dominated by on-shell evolution

Classical evolution accurately describes non-linear perturbations prior to horizon crossing

Provides criteria for when stochastic inflation reproduces quantum results

Abstract

We examine the classical and quantum evolution of inflationary cosmological perturbations from quantum initial conditions, using the on-shell and off-shell contributions to correlators to investigate the signatures of interactions. In particular, we calculate the Keldysh contributions to the leading order bispectrum from past infinity, showing that the squeezed limit is dominated by the on-shell evolution. By truncating the time integrals in the analytic expressions for contributions to the bispectrum, we define a `quantum interactivity' and quantitatively identify scales and times for which it is sufficient to only assume classical evolution, given a fixed precision. In contrast to typical perceptions inspired by free two-point functions, we show that common non-linear contributions to inflationary perturbations can be well-described by classical evolution even prior to horizon crossing. The insights gained here can pave the way for quantitative criteria for justifying the validity of numerically simulating the generation and evolution of quantum fluctuations in inflation. In particular, we comment on the validity of using stochastic inflation to reproduce known in-in perturbative results. An extensive appendix provides a review of the Keldysh formulation of the in-in formalism with the initial state set at a finite, as opposed to infinite past, emphasizing the importance of considering temporal boundary terms and the initial state for correctly obtaining the propagators. We also show how stochastic dynamics can emerge as a sufficiently accurate approximation to the full quantum evolution. This becomes particularly transparent in the Keldysh description.