Bouncing Universe with Quintom Matter

TL;DR

The paper tackles the Big Bang singularity by exploring non-singular bouncing cosmologies driven by Quintom matter in a 4D FRW framework. It analyzes three realizations—(i) a phenomenological EoS that crosses $w=-1$, (ii) a two-field Quintom with a canonical and a ghost scalar, and (iii) a single scalar with high-derivative Born-Infeld–type terms—to realize a bounce with NEC violation near the bounce and a post-bounce transition of the EoS to $w>-1$. The results include an explicit analytic solution for the phenomenological model and robust numerical bouncing solutions in the two-field and high-derivative models, all featuring $H$ crossing zero at the bounce and $w$ crossing $-1$ afterward. This work demonstrates that a non-singular bounce is feasible within standard Einstein gravity using Quintom matter, providing a bridge between early-universe dynamics and dark-energy phenomenology with connections to string-inspired tachyonic actions. The findings offer a framework for early-universe scenarios and potential links to post-bounce inflationary phases and observational signatures.

Abstract

The bouncing universe provides a possible solution to the Big Bang singularity problem. In this paper we study the bouncing solution in the universe dominated by the Quintom matter with an equation of state (EoS) crossing the cosmological constant boundary. We will show explicitly the analytical and numerical bouncing solutions in three types of models for the Quintom matter with an phenomenological EoS, the two scalar fields and a scalar field with a modified Born-Infeld action.

Figures (5)

• Figure 1: Plot of the evolution of the EoS $w$, the hubble parameter $H$ and the scale factor $a$ as a function of the cosmic time $t$. Here in the numerical calculation we have taken $r=0.6$ and $s=1$.
• Figure 2: The plots of the evolutions of the EoS $w$, hubble parameter $H$ and the scale factor $a$. In the numerical calculation we choose $V(\phi_1,\phi_2)=V_1 e^{-\lambda_1\frac{\phi_1^2}{M^2}}+V_2 e^{-\lambda_2\frac{\phi_2^2}{M^2}}$ with parameters: $V_1=15,~V_2=1,~\lambda_1=-1.0,~\lambda_2=1.0$, and for the initial conditions $\phi_1=0.5,~\dot\phi_1=0.1,~\phi_2=0.3,~\dot\phi_2=4$.
• Figure 3: The same plots as Fig. \ref{['fig:double']} with different potential and model parameters $V(\phi)=\frac{1}{2}m^2{\phi_1}^2+V_0{\phi_2}^{-2},~m=2,~V_0=0.4$, and for the initial conditions $\phi_1=2,~\dot\phi_1=3,~\phi_2=1,~\dot\phi_2=2$.
• Figure 4: The plots of the evolution of the EoS $w$, the hubble parameter $H$ and the scale factor $a$. Here in the numerical calculation we take the potential $V(\phi)=V_0e^{-\lambda\phi^2}$, $\alpha=-0.2$, $\beta=2$, $\lambda=2$, $V_0=5$, and the initial values are $\phi=1$, $\dot\phi=3$, $H=-1$, and $\psi=-80$.
• Figure 5: The plots of the evolutions of the EoS $w$, hubble parameter $H$ and the scale factor $a$. In the numerical calculation we choose the potential as $V(\phi)=\frac{V_0}{\phi}$, $\alpha=-0.2,~\beta=2,~V_0=0.7$, and for the initial conditions $\phi=10,~\dot\phi=-3,~H=-1,~\psi=-40$.