Evolution of Cosmological Perturbations in the Universe dominated by Resonant Scalar Fields

TL;DR

This paper extends a Hamiltonian approach to study cosmological perturbations in a universe dominated by resonant scalar fields, revealing conditions under which perturbations grow due to system instabilities.

Contribution

It introduces an analysis of scalar field resonance effects on cosmological perturbations using a canonical transformation to simplify the Hamiltonian.

Findings

Perturbations grow when the truncated Hamiltonian has hyperbolic fixed points.

The method effectively separates fast and slow dynamics in resonant scalar field systems.

Resonance can lead to instability and amplification of cosmological perturbations.

Abstract

Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on superhorizon scales in the case that the scalar fields have incommensurable masses. In the present paper, the analysis is extended to the case that the masses of the scalar fields satisfy resonance relations approximately. In this case, the action-angle variables for the system can be classified into fast changing variables and slowly changing variables. We show that after an appropriate canonical transformation, the part of the Hamiltonian that depends on fast changing angle variables can be made negligibley small, so that the dynamics of the system can be effectively determined by a truncated Hamiltonian that describes a closed dynamics of the slowly changing varables. Utilizing this formulation, we show that the system is unstable if this truncated Hamiltonian system has hyperbolic fixed point and as a consequence, the Bardeen parameter for a perturbation of the system grows.