Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models

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.

💡 Research Summary

This paper investigates whether anisotropic cosmological models can both avoid the classical singularity and suppress the growth of shear during contraction when the universe is driven by ekpyrotic potentials, without assuming that the system starts already in an ekpyrotic phase. The authors work within the effective spacetime description of Loop Quantum Cosmology (LQC), which replaces the classical Friedmann equations with modified differential equations that encode non‑perturbative quantum‑geometric effects. In LQC the energy density and anisotropic shear are bounded by universal maxima, leading to a generic, non‑singular bounce whenever the total density approaches the Planck scale.

Two classes of potentials are considered: a standard ekpyrotic potential V(φ)=−V₀ e^{−λφ} and a “ekpyrotic‑like” variant. Both generate an ultra‑stiff equation of state w≫1 when the scalar field rolls down the negative part of the potential, causing the scalar energy density to grow faster than the shear. The novelty of the study lies in the choice of initial conditions: the simulations start from a classical, macroscopic contracting universe with random values of the scalar field (φ∈