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Abstract In this paper, we study the quasi-normal modes (QNMs) of a scalar field in the background of a large class of quantum black holes that can be formed from gravitational collapse of a dust fluid in the framework of effective loop quantum gravity. The loop quantum black holes (LQBHs) are characterized by three free parameters, one of which is the mass parameter, while the other two are purely due to quantum geometric effects. Among these two quantum parameters, one is completely fixed by black hole thermodynamics and its effects are negligible for macroscopic black holes, while the second parameter is completely free (in principle). In the studies of the QNMs of such LQBHs, we pay particular attention to the difference of the QNMs between LQBHs and classical ones, so that they can be observed for the current and forthcoming gravitational wave observations, whereby place the LQBH theory directly under the test of observations. 

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. 

In this paper, we study cosmological perturbations in a modified theory of loop quantum cosmologies, the so-called mLQC-I model. Our purposes are two-fold: First, using a method developed by Birrell and Davies, we identify an initial state in the remote contracting phase, which turns out to be stable, minimize particle creations and diagonalize the Hamiltonian, despite the fact that at this time some modes may be still outside of the Hubble horizon and not in their adiabatic states. Second, using the uniform asymptotic approximation method, we obtain the first-order approximate solutions of the mode function in terms of either the Airy functions, or the first or second kind of cylindrical functions, depending on the values of the wavenumber. In each case, the mode function contains two integration constants, which are uniquely determined by the initial state. 

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. 

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. 

We study a multi-field model in Loop Quantum Cosmology for a maximally symmetric spacetime governed by the Einstein--Hilbert action minimally coupled to scalar fields. Using a Legendre transformation, we formulate the Hamiltonian dynamics in canonically equivalent geometrodynamical and Yang--Mills--type representations, incorporating nontrivial couplings through a geometric structure on the multi-field configuration space. Implementing the μ¯-scheme polymerization, we obtain the loop-quantum-corrected Friedmann equations. By focusing on the two-field model as an example, we analyze the effective dynamics for specific potentials. The quantum bouncing, transition, and slow-roll inflationary phases are investigated numerically, and viability of the models is assessed by evaluating the number of e-folds during the inflationary phase for certain given initial conditions. The global behavior of the background evolution is further examined through linear stability and dynamical-systems analyses. 

We investigate Power-Law Plateau (PLP) inflation in standard gravity and its consistency with ACT DR6 data. While many inflationary models, including the Starobinsky inflation, are disfavored by ACT observations, the PLP potential remains viable across a broad range of its parameters. Then, the dynamics of the reheating phase are investigated, where we mainly focus on the reheating temperature and its relationship with the inflationary phase and primordial gravitational waves. Incorporating the overproduction of the primordial gravitational waves can affect the effective number of relativistic species during the bounce. The constraint data on ΔNeff can impose a lower bound on the reheating temperature. This constraint will be more efficient for a stiff equation of state. It is determined that for ωre>0.58, this constraint would be efficient. Combining the result of the reheating temperature and the inflationary phase, it is concluded that to have both a viable result standing in 1σ of ACT DR6 and also to satisfy the reheating lower bound, the total number of e-folds during the inflationary phase should be Nk≲62. Higher e-folds of expansion result in a reheating temperature below the bound, which is disfavored. Finally, for the constraint values of the reheating temperature, the energy spectrum of the gravitational waves has been explored. The results indicate that there is a higher chance of detection for lower reheating temperatures and higher reheating equation of state. 

We study the dynamics of the Bianchi I universe in modified loop quantum cosmology (mLQC-I) and uncover a robust mechanism for isotropization: the shear is dynamically suppressed after the bounce and decays rapidly in the quantum post-bounce regime, independently of the equation of state of standard matter sources. This naturally drives the Universe toward a homogeneous and isotropic expanding phase without fine-tuning. Our results show that mLQC-I provides a new quantum-gravitational mechanism for suppressing anisotropies, absent in other bounce models.