Remarks on squeezed states of a harmonic oscillator in spatially flat Robertson-Walker space-time

Abstract

We have investigated the time evolution of a non-relativistic harmonic oscillator in a spatially flat Robertson-Walker background space-time. It is found that the time evolution operator of the system is a product of a squeeze operator and a rotation operator, and thus the initial cohrent state evolves into a squeezed state at a later time. In other words, the time evolution of the non-relativistic oscillator in a spatially flat Robertson-Walker background spacetime is a «squeezing» process. The squeezing effect is induced by the continuous scale dilation in expanding space-time, and depends on the specific model for an expanding universe. For instance, there is no squeezing in the de Sitter model, whereas squeezing does occur in the spatially flat Friedmann model.