On Perturbations of Quintom Bounce

TL;DR

The paper addresses perturbations in a nonsingular Quintom Bounce realized with two fields, one ghost, enabling NEC violation around the bounce. It derives perturbation equations in the longitudinal gauge and analyzes the evolution across heating, slow-climb-contracting, the bounce, and slow-roll-expanding phases, complemented by numerical simulations. A key result is that short-wavelength perturbations inherit the contracting-phase growing mode to the post-bounce dominant mode, while long-wavelength modes map to the decaying/constant modes in expansion, reflecting the different sub-Hubble histories. The work demonstrates that a Quintom bounce yields a non-singular, controllable perturbation evolution and may imprint distinctive signatures on cosmological perturbation spectra, while avoiding trans-Planckian concerns and connecting to both non-singular and singular bouncing literature.

Abstract

A Quintom universe with an equation-of-state crossing the cosmological constant boundary can provide a bouncing solution dubbed the Quintom Bounce and thus resolve the Big Bang singularity. In this paper, we investigate the cosmological perturbations of the Quintom Bounce both analytically and numerically. We find that the fluctuations in the dominant mode in the post-bounce expanding phase couple to the growing mode of the perturbations in the pre-bounce contracting phase.

Figures (9)

• Figure 1: Plot of the evolution of the Hubble parameter $H$ in the model (\ref{['lagrangian']}). In the numerical calculation we choose the initial values of parameters as: $\phi=-5.6\times10^{3},~\dot\phi=2.56\times10^{2},~\dot\psi=4.62\times10^{-73},~m=1.414\times10^{-1}$. The initial time was chosen to be $t = -500$. Note that in this and the following figures with results from numerical simulations, all masses are expressed in units of $10^{-6} M_{pl}$.
• Figure 2: Plot of the evolution of the EoS parameter $w$ in the model (\ref{['lagrangian']}). The initial values of parameters are the same as in Fig. \ref{['fig1:hubb']}.
• Figure 3: A sketch of the evolution of perturbations with different comoving wave numbers $k$ in the Quintom Bounce.
• Figure 4: A plot of the evolution of the factor $3H+\frac{\ddot\phi}{\dot\phi}$ in the bouncing phase.
• Figure 5: A sketch of the evolution of the gravitational potential $\Phi$ in the bouncing phase.