Effects of the ekpyrotic mechanism on inflationary phase in loop quantum cosmologies

TL;DR

This work tackles how an ekpyrotic mechanism, implemented via a negative near-bounce potential $V_{\text{ekp}}(\phi)$, modifies the generic inflationary behavior in loop quantum cosmologies. By coupling $V_{\text{ekp}}$ to a standard inflationary potential $V_{\text{inf}}$, the authors show that the ekpyrotic phase can dominate near the quantum bounce, driving $w_{\phi}>1$ and suppressing the shear, before the inflationary potential takes over and sustains a prolonged $N_{\text{inf}}$. The analysis across LQC and modified LQC-I reveals that the resulting viability and timing of inflation depend sensitively on the parameter choices for both potentials and the initial data $\phi_B,\dot{\phi}_B$, with scenarios featuring single or two inflation epochs (notably in mLQC-I) and several cases where $N_{\text{inf}}\gtrsim 60$ can be achieved. These findings underscore the importance of UV/Planck-scale physics in shaping pre- and post-bounce cosmology and motivate further study of perturbations and observational signatures arising from such ekpyrotic-assisted bounces.

Abstract

In bouncing cosmological models, either classical or quantum, the big bang singularity is replaced by a regular bounce. A challenging question in such models is how to keep the shear under control in the contracting phase, as it is well-known that the shear grows as fast as $1/a^{6}$ toward the bounce, where $a$ is the average expansion factor of the universe. A common approach is to introduce a scalar field with an ekpyrotic-like potential which becomes negative near the bounce, so the effective equation of state of the scalar field will be greater than one, whereby it dominates the shear in the bounce region. As a result, a homogeneous and isotropic universe can be produced after the bounce. In this paper, we study how the ekpyrotic mechanism affects the inflationary phase in both loop quantum cosmology (LQC) and a modified loop quantum cosmological model (mLQC-I), because in these frameworks inflation is generic without such a mechanism. After numerically studying various cases in which the potential of the inflaton consists of two parts, an inflationary potential and an ekpyrotic-like one, we find that, despite the fact that the influence is significant, by properly choosing the free parameters involved in the models, the ekpyrotic-like potential dominates in the bounce region, during which the effective equation of state is larger than one, so the shear problem is resolved. As the time continuously increases after the bounce, the inflationary potential grows and ultimately becomes dominant, resulting in an inflationary phase. This phase can last long enough to solve the cosmological problems existing in the big bang model.

Figures (14)

• Figure 1: The plot of the total potential $V(\phi)$ defined by Eq.(\ref{['eq3.5']}) with $U_0=0.0366$, $p=0.1$, $\beta=5$ and the chaotic inflationary potential given by Eq.(\ref{['eq3.11']}) with $\alpha_1 = \alpha_2 = 0,\; m = 1.26 \times 10^{-6}\; m_{P}$. The corresponding minimal and maximal values of $w_B$ are also given.
• Figure 2: The plot of the total number of e-folds with a chaotic potential given by Eq.(\ref{['eq3.11']}) where $\alpha_1=\alpha_2=0$ and $m = 1.26 \times 10^{-6}\; m_\text{pl}$, and an ekpyrotic potential given by Eqs.(\ref{['eq3.3']}) in the framework of LQC, where the parameters are chosen as $U_0=0.0366$, $p=0.1$, $\beta=5$. The plots (a) and (b) are for $\dot\phi_B>0$, while the plots (c) and (d) are for $\dot\phi_B< 0$. The plots (a) and (c) are for the case without the ekpyrotic potential (\ref{['eq3.3']}), and the plots (b) and (d) are for the cases with the ekpyrotic potential.
• Figure 3: The plots, (a) and (b), of the total number of e-folds as well as the plots, (c), of $\epsilon_H$ and, (d), energy density $\rho/\rho_c$ vs $t$ for $\phi_B = 2.502$ and the plot, (e) of $w_B$ vs. $\phi_B$ with a polynomial chaotic po$\alpha_1=\alpha_2=0$ and $m = 1.26 \times 10^{-6}\; m_\text{pl}$ and an ekpyrotic potential given by Eqs.(\ref{['eq3.3']}) in the framework of LQC, where the parameters are chosen as $U_0=0.366$, $p=0.05$, $\beta=0.1$ in LQC for $\dot\phi_B>0$. The plot (a) is the case in which the ekpyrotic potential (\ref{['eq3.3']}) is turned off, while the plots (b), (c), (d), and (e) are the case in which the ekpyrotic potential is turned on.
• Figure 4: The plots of the total number of e-folds with $\dot\phi_B >0$ and $\dot\phi_B < 0$ in LQC only when the polynomial chaotic potential given by Eq.(\ref{['eq3.11']}) is present with the choice $\alpha_1 = 0.14, \; \alpha_2 = 6.644 \times 10^{-3}$ and $m = 1.26 \times 10^{-6}\; m_\text{pl}$Kallosh:2025ijd. The plot (a) is for $\dot\phi_B>0$, while the pot (b) is for $\dot\phi_B< 0$.
• Figure 5: The plots, (a) and (b), of the total number of e-folds as well as the plots, (c), of $\epsilon_H$ and, (d), energy density $\rho/\rho_c$ vs $t$ for $\phi_B = 0.652$ and the plot, (e) of $w_B$ vs. $\phi_B$ with a polynomial chaotic potential given by Eq.(\ref{['eq3.11']}) where $\alpha_1 = 0.14, \;\alpha_2 = 6.644 \times 10^{-3},$ and $m = 1.26 \times 10^{-6}\; m_\text{pl}$ and an ekpyrotic potential given by Eqs.(\ref{['eq3.3']}) in the framework of LQC, where the parameters are chosen as $U_0=10^3$, $p=0.1$, $\beta=1$ for the $\dot\phi_B>0$ case. The plot (a) is the case in which the ekpyrotic potential (\ref{['eq3.3']}) is turned off, while the plots (b), (c), (d), and (e) are the case in which the ekpyrotic potential is turned on.