Classicality of the primordial perturbations

TL;DR

The paper addresses how primordial quantum fluctuations transition to classical seeds during inflation. It shows that once a mode satisfies the WKB realness criterion for superhorizon scales, classicality persists to all orders by analyzing the interacting evolution with $U(t)=T\exp(-i\int \hat{H}_I dt)$ and demonstrating that $U\to 1$ and the auxiliary term $B\to 0$ in perturbation theory. The key contributions include establishing the equivalence between real mode functions and vanishing commutators $[\hat{\phi}_{\rm hp}, \hat{\phi}_{\rm hp}']$, extending the argument to higher order via the in--in formalism, and showing that correlators can be expressed in terms of an effective classical field $\delta\phi^{\rm cl}$ with the curvature perturbation $\zeta$ computed through a combination of Q- and C-Feynman diagrams, linked by the $\delta N$ expansion. This framework clarifies how different slicings (flat vs uniform-density) yield equivalent results at tree level and provides a practical approach to non-Gaussianity calculations, while highlighting that loop effects remain challenging. Overall, the work unifies quantum and classical descriptions of inflationary perturbations and clarifies the conditions under which a quantum-to-classical transition governs the late-time structure formation.

Abstract

We show that during inflation, a quantum fluctuation becomes classical at all orders if it becomes classical at first order. Implications are discussed.