scholarly journals A CRITICAL ANALYSIS OF THE COSMOLOGICAL IMPLEMENTATION OF LOOP QUANTUM GRAVITY

2012 ◽  
Vol 27 (07) ◽  
pp. 1250032 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Critical Discussion ◽  
Point Of View ◽  
Graph Structure ◽  
Quantum Geometry ◽  
Cosmological Problem ◽  
New Perspective ◽  
Made In

This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the isotropic Universe, we trace a new perspective in approaching the cosmological problem within quantum geometry. The cosmological sector of LQG is reviewed and a critical point of view on LQC is presented. It is outlined how a polymer-like scale for quantum cosmology can be predicted from a proper fundamental graph underlying the homogeneous and isotropic continuous picture. However, such a minimum scale does not coincide with the choice made in LQC. Finally, the perspectives towards a consistent cosmological LQG model based on such a graph structure are discussed.

scholarly journals Quantum Geometry II : The Mathematics of Loop Quantum Gravity Three dimensional quantum gravity

2020 ◽  
Author(s):  
J. Manuel Garcia-Islas
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Physical Theory ◽  
Loop Quantum Gravity ◽  
Three Dimensional ◽  
Point Of View ◽  
Quantum Geometry ◽  
Mathematical Task ◽  
Postgraduate Students ◽  
And Mathematics

Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and departing from such theory quantise it. General relativity describes gravity in terms of geometry. Therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well. This is why in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three dimensional case.

scholarly journals Quantum Geometry I: Basics of Loop Quantum Gravity

2019 ◽  
Vol 65 (1) ◽  
pp. 7
Author(s):  
J. Manuel García-Islas
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Point Of View ◽  
Quantum Geometry ◽  
And Mathematics ◽  
Area Of Study

General Relativity describes gravity in geometrical terms. This sug-gests that quantising such theory is the same as quantising geometry.The subject can therefore be called quantum geometry and one maythink that mathematicians are responsible of this subject. Unfortunatelymost mathematicians are not aware of this beautiful area of study. Herewe give a basic introduction to what quantum geometry means to a com-munity working in a theory known as loop quantum gravity. It is directedtowards graduate or upper students of physics and mathematics. We doit so from a point of view of a mathematician.

Polymer quantization effects on gauge-flation

2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Abelian Gauge ◽  
Friedmann Equations ◽  
Cosmological Inflation

Polymer quantum mechanics, as a non-standard representation of quantum mechanics, is based on a symmetric sector of loop quantum gravity known as loop quantum cosmology. In this work, by analyzing the Hamiltonian and Friedmann equations in the standard Hilbert space and polymer Hilbert space, we show that polymer quantization is a successful formalism for a non-Abelian gauge field driving the cosmological inflation, the so-called gauge-flation, in order to remove initial singularity and also keeping the inflationary trajectories in this model as attractors of dynamics after the bounce.

scholarly journals Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 41 ◽  
Author(s):  
Bekir Baytaş ◽  
Martin Bojowald ◽  
Sean Crowe
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Canonical Realization ◽  
Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

scholarly journals Quantum reduced loop gravity and the foundation of loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642005 ◽  
Author(s):  
Emanuele Alesci ◽  
Francesco Cianfrani
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Quantum Description ◽  
Semiclassical Dynamics ◽  
Loop Gravity ◽  
The Universe

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 a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.

scholarly journals HOLOGRAPHY FROM LOOP QUANTUM GRAVITY

2008 ◽  
Vol 17 (03n04) ◽  
pp. 545-549 ◽  
Author(s):  
RODOLFO GAMBINI ◽  
JORGE PULLIN
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Basic Structure ◽  
Spherically Symmetric ◽  
Quantum Geometry ◽  
Amount Of Information

We show that holography follows directly from the basic structure of spherically symmetric loop quantum gravity. The result is not dependent on detailed assumptions about the dynamics of the theory being considered. It ties strongly the amount of information contained in a region of space to the tight mathematical underpinnings of loop quantum geometry.

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