Related papers: On the Configuration Spaces of Homogeneous Loop Qu…
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited…
In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop…
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner.…
Given a group $G$ and an abelian $C^*$-algebra $\mathfrak{A}$, the antihomomorphisms $\Theta\colon G\rightarrow \mathrm{Aut}(\mathfrak{A})$ are in one-to-one with those left actions $\Phi\colon G\times \mathrm{Spec}(\mathfrak{A})\rightarrow…
In loop quantum gravity in the connection representation, the quantum configuration space $\bar{\mathcal{A}/\mathcal{G}}$, which is a compact space, is much larger than the classical configuration space $\mathcal{A}/% \mathcal{G}$ of…
Loop Quantum Cosmology adapts the techniques of Loop Quantum Gravity in the quantization of homogeneous cosmological models obtained from General Relativity by symmetry reduction. As a necessary step towards the extraction of realistic…
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…
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure…
The article gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the corresponding configuration space…
A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
The global dynamics of a homogeneous universe in Loop Quantum Cosmology is viewed as a scattering process of its geometrodynamical equivalent. This picture is applied to build a flexible (easy to generalize) and not restricted just to…
A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…