Related papers: Loop Quantum Cosmology II: Volume Operators
We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…
We do not observe quantum effects on cosmological scales. Thus, if loop quantum cosmology (LQC) is to provide an accurate depiction of the real world, it must allow for quantum states of spacetime geometry which are semi-classical in two…
Ambiguities of the so-called Thiemann regularization in Loop Quantum Cosmology lead to freedom in how to construct a particular quantization prescription. So far three distinct examples of such have been proposed in the literature. For two…
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint…
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level.…
The standard toolkit of operators to probe quanta of geometry in loop quantum gravity consists in area and volume operators as well as holonomy operators. New operators have been defined, in the U(N) framework for intertwiners, which allow…
We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum…
We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff, include terms that favour the breaking of translation…
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…
First, we review the $C^\ast$-algebraic foundations of loop quantization, in particular, the construction of quantum configuration spaces and the implementation of symmetries. Then, we apply these results to loop quantum gravity, focusing…
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…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a…
We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator.…
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that…
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the…
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…
This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the physics of computation to ensembles of clocks, as in GPS, we present a covariant version of the…
For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained from loop quantum gravity, has shed new…
This chapter provides a review of the frameworks developed for cosmological perturbation theory in loop quantum cosmology, and applications to various models of the early universe including inflation, ekpyrosis and the matter bounce, with…