Inflation and squeezed quantum states

TL;DR

This paper analyzes inflationary perturbations through the framework of squeezed quantum states, deriving a two-mode squeezing description for each Fourier mode and expressing the evolution in terms of the squeezing parameters $R_{\vec{k}}$, $\Phi_{\vec{k}}$, and $\Theta_{\vec{k}}$. It shows that, while the formalism provides an intuitive and systematic picture of amplification via squeezing, the resulting predictions (e.g., the power spectrum on superhorizon scales and acoustic features) align with standard, largely classical descriptions, with desqueezing and Sakharov oscillations arising from well-known dynamics rather than novel quantum effects. Through analytic and numerical analyses in a simple inflationary model, the work clarifies the role of strong vs. weak coupling, the Bunch–Davies vacuum as an attractor, and the transition to a hydrodynamic era, illustrating that the squeezed-state viewpoint is a useful reformulation rather than a source of new physics. The conclusions emphasize that cosmological perturbations at late times are effectively semiclassical, and that the squeezed-state formalism, while insightful, does not introduce new physical predictions beyond those of the standard treatment.

Abstract

The inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a process of quantum squeezing. We carefully develop the squeezed state formalism and derive the equations that govern the evolution of a gaussian initial state. We derive the power spectrum of density perturbations for a simple inflationary model and discuss its features. We conclude that the squeezed state formalism provides an interesting framework within which to study the amplification process, but,in disagreement with the claims of Grishchuk and Sidorov, that it does {\em not} provide us with any new physical results.