Related papers: The two-vertex model of loop quantum gravity: anis…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We develop the "triangulated" version of loop quantum cosmology, recently introduced in the literature. We focus on the "dipole" cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
In this manuscript, we address the issue of the loss of SU(2) internal symmetry in Loop Quantum Cosmology and its relationship with Loop Quantum Gravity. Drawing inspiration from Yang-Mills theory and employing the framework of fiber bundle…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
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…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
We present a class of theories of two dimensional gravity which admits homogeneous and isotropic solutions that are nonsingular and asymptotically approach a FRW matter dominated universe at late times. These models are generalizations of…
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We discuss scaling relations in four dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called ``baby universe surgery'' we study the critical region of the theory. The position of the phase…
We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once…
Anisotropic cosmological models are investigated in the frame work of $f(R)$ gravity in the metric formalism. Plane symmetric models are considered to incorporate anisotropy in the expansion rates along different spatial directions. The…
We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions. By tuning anisotropic coupling strengths along distinct directions, we can manipulate the…
We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in…
The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg…
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present…