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We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
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…
We achieve a group theoretical quantization of the flat Friedmann-Robertson-Walker model coupled to a massless scalar field adopting the improved dynamics of loop quantum cosmology. Deparemeterizing the system using the scalar field as…
Since the past Iagrg meeting in December 2004, new developments in loop quantum cosmology have taken place, especially with regards to the resolution of the Big Bang singularity in the isotropic models. The singularity resolution issue has…
In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the…
We analyze the big bounce transition of the quantum FRW model in the setting of the nonstandard loop quantum cosmology (LQC). Elementary observables are used to quantize composite observables. The spectrum of the energy density operator is…
We provide a complete quantization for the Gowdy model with local rotational symmetry in vacuum. We start with a redefinition of the classical constraint algebra such that the Hamiltonian constraint has a vanishing Poisson bracket with…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
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 Immirzi parameter is promoted to be a scalar field and the Hamiltonian analysis of the corresponding dynamical system is performed in the presence of gravity. We identified some SU(2) connections, generalizing Ashtekar-Barbero…
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties…
The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The…
In this work we analyze the evolution of the quantum Mixmaster cosmological model within an effective approach. In particular, we study the behaviour of the scale factor and anisotropies of the theory, and determine how it deviates from its…
Modification to the behavior of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale…
It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine tuned. We show that the corrections to the equations of motion for the…
Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require…
Quantum cosmology may restrict the class of gauge models which unify electroweak and strong interactions. In particular, if one studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background…
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.…