Related papers: Discretisation parameter and operator ordering in …
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
In this work, we extend the formalism of hybrid loop quantum cosmology for primordial perturbations around a flat, homogeneous, and isotropic universe to the new treatment of Friedmann-Lema\^itre-Robertson-Walker geometries proposed…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to…
3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete model characterizes discrete flat geometries…
A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient…
We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the…
A previous paper constructed a kinematic basis for spin networks with planar or cylindrical symmetry and arbitrary polarization. This paper imposes a constraint which limits the gravitational wave to a single polarization. The spectrum of…
Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering…
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint…
We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization…
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…
We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in…
The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, quantum…
Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex - ``an atom of…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
A finite and unitary nonlocal formulation of quantum gravity is applied to the cosmological constant problem. The entire functions in momentum space at the graviton-standard model particle loop vertices generate an exponential suppression…
We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…