Related papers: Mathematical Structure of Loop Quantum Cosmology: …
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
The issue of consistency is crucial in quantum gravity. It has recently been intensively addressed for effective symmetry-reduced models. In this article, we exhaustively study the anomaly freedom of effective loop quantum cosmology with…
In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and,…
Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection…
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler…
We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
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 study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…
A well-motivated extension of higher order holonomy corrections in loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model is investigated at the level of heuristic effective dynamics. It reveals that the quantum bounce…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
In loop quantum cosmology, ambiguities in the Hamiltonian constraint can result in models with varying phenomenological predictions. In the homogeneous isotropic models, these ambiguities were settled, and the improved dynamics was found to…
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 standard model of cosmology assumes that the Universe can be described to hover around a homogeneous-isotropic solution of Einstein's general theory of relativity. This description needs (sometimes hidden) hypotheses that restrict the…
On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…