Perturbations in Symmetric Lee-Wick Bouncing Universe

TL;DR

This paper analyzes tensor and scalar perturbations in a symmetric Lee-Wick bouncing universe, revealing growth and decay behaviors, and providing spectral index calculations and perturbation evolution insights.

Contribution

It presents a detailed analytical study of perturbations in a Lee-Wick bouncing universe, including tensor mode functions and scalar perturbation behavior, extending previous numerical work.

Findings

Tensor perturbation grows during contraction and decays during expansion.

Tensor spectral index is calculated as n_T=6.

Scalar curvature remains constant on super-horizon scales and decays on sub-horizon scales.

Abstract

We investigate the tensor and the scalar perturbations in the symmetric bouncing universe driven by one ordinary field and its Lee-Wick partner field which is a ghost. We obtain the even- and the odd-mode functions of the tensor perturbation in the matter-dominated regime. The tensor perturbation grows in time during the contracting phase of the Universe, and decays during the expanding phase. The power spectrum for the tensor perturbation is evaluated and the spectral index is given by $n_{\rm T} =6$. We add the analysis on the scalar perturbation by inspecting the even- and the odd-mode functions in the matter-dominated regime, which was studied numerically in our previous work. We conclude that the comoving curvature by the scalar perturbation is constant in the super-horizon scale and starts to decay in the far sub-horizon scale while the Universe expands.