Related papers: On loop quantum gravity kinematics with non-degene…
Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann-Lemaitre-Robertson-Walker line element, we review how the background of holonomy corrected Loop Quantum Cosmology (LQC)…
Loop quantum gravity methods are applied to a symmetry-reduced model with homogeneity in two dimensions, derived from a Gowdy model [5,6]. The conditions for propagation of unidirectional plane gravitational waves at exactly the speed of…
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides…
The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this…
We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the…
Emergent modified gravity has shown that the canonical formulation of general relativity gives rise to a larger class of covariant modifications than action-based approaches, so far in symmetry-reduced models. This outcome is made possible…
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the…
In this article we present a brief introduction to the kinematical setup that underlies the quantization used in loop quantum gravity. This review has been published as a chapter in the monograph "Loop Quantum Gravity: The First 30 Years",…
We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…
We analyze the problem of general covariance for quantum gravity theories in the background field formalism with respect to gauge fixing procedure. We prove that the background effective action is not invariant under general coordinate…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
Cosmology appears as the most promising way to test and constrain quantum gravity theories. Loop quantum gravity is among the most advanced attempts to perform a non-perturbative quantization of general relativity. Its cosmological…
The loop quantization of 3d gravity consists in defining the Hilbert space of states satisfying the Gau{\ss} constraint and the flatness constraint. The Gau{\ss} constraint is enforced at the kinematical level by introducing spin networks…
We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in…
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\em directly at the quantum level}. Such a firmer understanding would…