Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models

TL;DR

The paper examines whether ekpyrotic and ekpyrotic-like potentials can dynamically isotropize anisotropic, nonsingular bouncing universes within the effective dynamics of loop quantum cosmology. Using extensive numerical simulations for Bianchi-I and Bianchi-IX spacetimes, it compares ekpyrotic scenarios to a massless scalar reference across two potential strengths, revealing that isotropization is achieved in the majority of cases, often via brief ekpyrotic phases during rapid, multiple quantum bounces. A key finding is that increasing the ekpyrotic potential strengthens isotropization in Bianchi-I, while in Bianchi-IX the effect remains robust but more nuanced due to curvature, with strong isotropization observed even for ekpyrotic-like potentials. Overall, the results support ekpyrosis as a robust mechanism for damping anisotropies in bouncing cosmologies, with potential implications for generic early-universe dynamics and perturbation evolution in quantum gravity settings.

Abstract

We explore the isotropization of a model anisotropic universe in the bouncing models using the ekpyrotic potential without assuming initial conditions corresponding to an ekpyrotic phase. In particular, we explore the way the use of ekpyrotic potentials may dynamically help isotropization for the considered initial conditions corresponding to the macroscopic classical contracting universe with potentially large anisotropies. As an example of a concrete nonsingular bouncing mechanism, we consider the effective description of loop quantum cosmology for Bianchi-I and Bianchi-IX spacetimes for ekpyrotic and ekpyrotic-like potentials. Considering two different values of potential parameters and initial conditions corresponding to a classical macroscopic universe, we show that for both of these spacetimes, the cosmological singularity is resolved via multiple short-duration nonsingular bounces caused by quantum gravitational effects. We perform a large number of numerical simulations for a wide range of initial conditions which do not favor ekpyrosis initially. Even with such unfavorable initial conditions, we show that the relative strength of the anisotropies at the end of the bounce regime is noticeably reduced in more than 90% of the simulations. This provides a strong evidence for the isotropization ability of the ekpyrotic potentials. We find that isotropization can occur over cycles of rapid nonsingular bounces in the Planck regime via enhancement of the contribution of the (isotropic) energy density relative to the anisotropies at the bounces. Achieving isotropization is found to be easier in Bianchi-I spacetimes when compared to Bianchi-IX spacetimes. Our results demonstrate that, even with initial conditions which are not most favorable for the existence of ekpyrosis, an effective isotropization can occur in nonsingular anisotropic models with ekpyrotic and ekpyrotic-like potentials.

Figures (13)

• Figure 1: An example of the non-singular evolution of directional scale factors, equation of state, energy density and anisotropic shear in the bounce regime for effective Bianchi-I spacetime coupled to the ekpyrotic scalar field with $U_0 = 0.25$ in \ref{['Ekpyrotic_potential']}. If one considers time from negative to positive three scale factors are decreasing before $t = 0$ and then two are increasing while one is decreasing after the bounce. The universe has a point like approach to singularity which after resolution due to quantum geometry effects yields a cigar like evolution as is generally the case for Kasner transitions in LQC Gupt:2012vi. It is typical to get multiple bounces before the universe eventually enters a macroscopic expanding regime. Unlike the classical theory, the scale factors have finite nonzero values throughout the evolution and the energy density and anisotropic shear do not diverge. These features are seen in all simulations discussed in this manuscript.
• Figure 2: The time evolution of the pressure and potential and kinetic energies corresponding to the example shown in Figure 1. In the case of the ekpyrotic scalar field, the pressure remains positive definite.
• Figure 3: Bianchi-I effective spacetime with an ekpyrotic field having $U_0 = 0.25$: comparison of energy density $\rho_\mathrm{b}/\rho_\mathrm{max}$, shear $\sigma_\mathrm{b}^2/\sigma_\mathrm{max}^2$, and the relative strength of anisotropies $R_\sigma$ at the last bounce in case of the ekpyrotic potential (y-axis) versus the massless scalar case (x-axis) for 500 simulations with matching initial conditions. The dots represent one simulation each, and the diagonal line $(x=y)$ is shown for ease of comparison. The dots in the first and second panel are color coded to provide additional information. The same color coding is used in all comparison plots in this manuscript. The blue dots in the energy density plot represent simulations where the shear scalar at the bounce increased relative to the massless case. Similarly, the blue dots in shear scalar plot represent simulations where energy density at the bounce was higher relative to the corresponding massless case. The red dots represent simulation with the opposite trend. We see here that the energy density at the bounce increased compared to the massless case in all the simulations whereas the shear is not necessarily decreased in all the simulations. Nevertheless, the $R_\sigma$ plot shows that the relative strength of anisotropies decreased in all the simulations.
• Figure 4: Bianchi-I effective spacetime with an ekpyrotic field ($U_0 = 1.25$): comparison of energy density $\rho_\mathrm{b}/\rho_\mathrm{max}$, shear $\sigma_\mathrm{b}^2/\sigma_\mathrm{max}^2$, and the relative strength of anisotropies $R_\sigma$ at the last bounce between the ekpyrotic potential (y-axis) and the massless scalar case (x-axis) with matching initial conditions. Each plot contains 500 dots representing one simulation each. The color coding scheme used for dots in the energy density and shear scalar plots is the same as in the previous figure.
• Figure 5: The typical evolution of directional scale factors, equation of state, energy density and anisotropic shear in the bounce regime for effective Bianchi-I spacetime coupled to the ekpyrotic-like scalar field with $U_0 = 0.25$. The number of bounces obtained is usually lower compared to the case of ekpyrotic field.