The status of quantum geometry in the dynamical sector of loop quantum cosmology

Kamiński, Wojciech; Lewandowski, Jerzy; Szulc, Łukasz

doi:10.1088/0264-9381/25/5/055003

Cited by 11 publications

(12 citation statements)

References 34 publications

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“…In order to define the decomposition in a precise form, we first introduce the following transformation of the eigenfunctions of Θ 1 , defined in the distributional sense on each of the subsemilattices (4) L + ε1 and (4) L + ε1+2 separately: [12,15]:…”

Section: V1-observables On Componentsmentioning

confidence: 99%

“…LQC has been further extended, with diverse levels of rigor, to other similar models with different topology [6] or nonvanishing cosmological constant [7], and furthermore to more general settings such as anisotropic systems [8,9,10], or even to inhomogeneous situations [11]. The robustness of the singularity resolution features has been confirmed within an exactly solvable version of LQC [12,13,14], and the mathematical foundations of its elements have been discussed [15,16]. In addition to the studies of the genuine quantum theory, there exists an extensive amount of work at the level of the effective classical dynamics [17,18], which provides important insights into the properties of the quantum geometry in cosmological scenarios [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Physical evolution in loop quantum cosmology: The example of the vacuum Bianchi I model

2009

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We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time. In order to retrieve the system dynamics when no such a suitable clock field is present, we explore different constructions of families of unitarily related partial observables. These observables are parameterized, respectively, by: (i) one of the components of the densitized triad, and (ii) its conjugate momentum; each of them playing the role of an evolution parameter. Exploiting the properties of the considered example, we investigate in detail the domains of applicability of each construction. In both cases the observables possess a neat physical interpretation only in an approximate sense. However, whereas in case (i) such interpretation is reasonably accurate only for a portion of the evolution of the universe, in case (ii) it remains so during all the evolution (at least in the physically interesting cases). The constructed families of observables are next used to describe the evolution of the Bianchi I universe. The performed analysis confirms the robustness of the bounces, also in absence of matter fields, as well as the preservation of the semiclassicality through them. The concept of evolution studied here and the presented construction of observables are applicable to a wide class of models in LQC, including quantizations of the Bianchi I model obtained with other prescriptions for the improved dynamics.

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Section: V1-observables On Componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Physical evolution in loop quantum cosmology: The example of the vacuum Bianchi I model

2009

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“…While the topic of the isotropic and homogeneous sector of the LQC originated in [6] is well understood [15,16,17,18,19,20,21] there still is work to be done in the homogeneous, but nonisotropic sector. Although loop quantum dynamics is not fully understood in this sector, already the first calculations in the quantum homogeneous models [7,8] suggest a completely different structure of the space-time near classical singularities.…”

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confidence: 99%

Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems

Szulc

2008

Phys. Rev. D

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A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to theμ scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of theμ scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of theμ scheme to the Bianchi I model do not imply limitations of theμ scheme in the isotropic case.

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“…Thus, for example, we have lim →0 lim t 0 A(D( , t)) = 8πβl 2 P j u (j u + 1) id (IV. 20) in general. One could argue that a natural definition of this limit would be given by the right hand side of the previous equation.…”

Section: Entropy Gradient For J D =60mentioning

confidence: 99%

Geometry and entanglement entropy of surfaces in loop quantum gravity

2018

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In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature and mean curvature. By investigating their properties, we shed light on the nature of the geometry of surfaces in loop quantum gravity.We also investigate the entanglement entropy across surfaces in the case where spin network edges are running within the surface. We observe that, on a certain class of states, the entropy gradient across a surface is proportional to the mean curvature. In particular, the entanglement entropy is constant for small deformations of a minimal surface in this case. CONTENTS

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The status of quantum geometry in the dynamical sector of loop quantum cosmology

Cited by 11 publications

References 34 publications

Physical evolution in loop quantum cosmology: The example of the vacuum Bianchi I model

Physical evolution in loop quantum cosmology: The example of the vacuum Bianchi I model

Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems

Geometry and entanglement entropy of surfaces in loop quantum gravity

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