scholarly journals Quantum reduction to Bianchi I models in loop quantum gravity

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
N. Bodendorfer
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Bianchi I ◽  
Quantum Reduction

scholarly journals A quantum reduction to spherical symmetry in loop quantum gravity

2015 ◽  
Vol 747 ◽  
pp. 18-21 ◽  
Author(s):  
N. Bodendorfer ◽  
J. Lewandowski ◽  
J. Świeżewski
Keyword(s):  
Quantum Gravity ◽  
Spherical Symmetry ◽  
Loop Quantum Gravity ◽  
Quantum Reduction

scholarly journals An Overview on the Nature of the Bounce in LQC and PQM

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 327
Author(s):  
Gabriele Barca ◽  
Eleonora Giovannetti ◽  
Giovanni Montani
Keyword(s):  
Energy Density ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Critical Energy ◽  
Loop Quantum Cosmology ◽  
Isotropic Universe ◽  
Bianchi I ◽  
Critical Energy Density ◽  
The Universe

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

scholarly journals The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

2012 ◽  
Vol 99 (1) ◽  
pp. 10003 ◽  
Author(s):  
F. Cianfrani ◽  
A. Marchini ◽  
G. Montani
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Bianchi I ◽  
Gauge Fixing

scholarly journals Review on hermiticity of the volume operators in Loop Quantum Gravity

2019 ◽  
Vol 51 (5) ◽  
Author(s):  
S. Ariwahjoedi ◽  
I. Husin ◽  
I. Sebastian ◽  
F. P. Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity

scholarly journals Quantum gravity: A brief history of ideas and some prospects

2015 ◽  
Vol 24 (11) ◽  
pp. 1530028 ◽  
Author(s):  
Steven Carlip ◽  
Dah-Wei Chiou ◽  
Wei-Tou Ni ◽  
Richard Woodard
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Black Hole Thermodynamics ◽  
History Of Ideas ◽  
Foreseeable Future ◽  
Gravitational Effects ◽  
History Of

We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity (LQG) and black hole thermodynamics. The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed.

Sign in / Sign up

Export Citation Format

Share Document