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We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of…
The cosmological singularities of the Bianchi I universe are analyzed in the setting of loop geometry underlying the loop quantum cosmology. We solve the Hamiltonian constraint of the theory and find the Lie algebra of elementary…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…
We analyze the loop quantization of the family of vacuum Bianchi I spacetimes, a gravitational system whose classical solutions describe homogeneous anisotropic cosmologies. We rigorously construct the operator that represents the…
We develop the "triangulated" version of loop quantum cosmology, recently introduced in the literature. We focus on the "dipole" cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the…
Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it…
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved…
We show how Loop Quantum Cosmology can be derived as an effective semiclassical description of Loop Quantum Gravity. Using the tools of QRLG, a gauge fixed version of LQG, we take the coherent states of the fundamental microscopic theory…
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced…
Quantum Reduced Loop Gravity provides a promising framework for a consistent characterization of the early Universe dynamics. Inspired by BKL conjecture, a flat Universe is described as a collection of Bianchi I homogeneous patches. The…
The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is considered. The first objective of this study is to investigate Einstein equations using a tractable assumption usually accepted in the…
We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor $F_{\mu\nu}$; the…
The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is…
Loop quantum cosmology leads to a difference equation for the wave function of a universe, which in general has solutions changing rapidly even when the volume changes only slightly. For a semiclassical regime such small-scale oscillations…
In classical general relativity, the generic approach to the initial singularity is very complicated as exemplified by the chaos of the Bianchi IX model which displays the generic local evolution close to a singularity. Quantum gravity…
A new mathematical framework is formulated to derive the effective equations of motion for the constrained quantum system which possesses an internal clock. In the realm close to classical behavior, the quantum evolution is approximated by…
Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the…
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models…