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1. Genericness of quantum damping of cosmological shear in modified loop quantum cosmology

   Gan, Wen-Cong; Graef, Leila L; Ramos, Rudnei O; Vicente, Gustavo S; Wang, Anzhong (April 2026, ArXivorg)

   In arXiv:2603.18175, the authors argue, based on numerical studies of particular cases, that the quantum damping of cosmological shear in a modified loop quantum cosmological model (mLQC-I) that was recently found in arXiv:2510.14021 is not generic and that the universe never becomes truly classical. In this brief Note, we revisit these claims by carefully examining the underlying assumptions and the class of initial conditions considered. We show that the examples analyzed in arXiv:2603.18175 correspond to configurations that do not represent physically admissible collapsing Bianchi I universes, as they involve mixed expanding-contracting directions and lead to effectively lower-dimensional post-bounce geometries. Restricting to physically relevant initial conditions corresponding to genuine three-dimensional contraction, we find that the quantum damping of cosmological shear is a robust dynamical feature. This conclusion is supported by both numerical and perturbative analyses, which demonstrate that the post-bounce evolution admits an isotropic attractor, with anisotropies decaying exponentially and independently of the matter content, provided that the weak energy condition is satisfied. We further outline a plausible post-bounce mechanism for the onset of classicalization. 

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

   Brown, Christian; Fier, Jared; Phillips, Brian; Cleaver, Gerald; Wang, Anzhong (March 2026, APS)

   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/a6 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. 

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

   Brown, Christian; Fier, Jared; Phillips, Brian; Cleaver, Gerald; Wang, Anzhong (August 2026, ArXivorg)

   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/a6 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. 

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4. Universal Properties of the Evolution of the Universe in Modified Loop Quantum Cosmology

   https://doi.org/10.3390/universe10100397  

   Saeed, Jamal; Pan, Rui; Brown, Christian; Cleaver, Gerald; Wang, Anzhong (October 2024, Universe)

   In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, w(ϕ)≃1. Soon, the inflation potential takes over, so w(ϕ) rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials. 

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5. A diffeomorphism invariant family of metric-affine actions for loop cosmologies

   https://doi.org/10.1088/1475-7516/2023/06/059  

   Delhom, Adrià; Olmo, Gonzalo J.; Singh, Parampreet (June 2023, Journal of Cosmology and Astroparticle Physics)

   Abstract In loop quantum cosmology (LQC) the big bang singularity is generically resolved by a big bounce. This feature holds even when modified quantization prescriptions of the Hamiltonian constraint are used such as in mLQC-I and mLQC-II. While the later describes an effective description qualitatively similar to that of standard LQC, the former describes an asymmetric evolution with an emergent Planckian de-Sitter pre-bounce phase even in the absence of a potential. We consider the potential relation of these canonically quantized non-singular models with effective actions based on a geometric description. We find a 3-parameter family of metric-affinef(ℛ) theories which accurately approximate the effective dynamics of LQC and mLQC-II in all regimes and mLQC-I in the post-bounce phase. Two of the parameters are fixed by enforcing equivalence at the bounce, and the background evolution of the relevant observables can be fitted with only one free parameter. It is seen that the non-perturbative effects of these loop cosmologies are universally encoded by a logarithmic correction that only depends on the bounce curvature of the model. In addition, we find that the best fit value of the free parameter can be very approximately written in terms of fundamental parameters of the underlying quantum description for the three models. The values of the best fits can be written in terms of the bounce density in a simple manner, and the values for each model are related to one another by a proportionality relation involving only the Barbero-Immirzi parameter. 

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