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

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.

2016 ◽  
Vol 25 (08) ◽  
pp. 1642005 ◽  
Author(s):  
Emanuele Alesci ◽  
Francesco Cianfrani

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.


2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari

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.


Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 41 ◽  
Author(s):  
Bekir Baytaş ◽  
Martin Bojowald ◽  
Sean Crowe

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.


2016 ◽  
Vol 25 (08) ◽  
pp. 1642008 ◽  
Author(s):  
Aurélien Barrau ◽  
Boris Bolliet

Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially critical when dealing with cosmological perturbations. The present paper reviews several approaches to the problem of building a consistent formalism that describes the dynamics of perturbations on a quantum spacetime and tries to address their respective strengths and weaknesses. We also review the main open issues in loop quantum cosmology.


2016 ◽  
Vol 25 (08) ◽  
pp. 1642003 ◽  
Author(s):  
Julien Grain

Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized [Formula: see text]-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.


2014 ◽  
Vol 24 (01) ◽  
pp. 1530005 ◽  
Author(s):  
Dah-Wei Chiou

This paper presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) — a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the paper, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered briefly. Current directions and open issues are also summarized.


2016 ◽  
Vol 25 (08) ◽  
pp. 1642010 ◽  
Author(s):  
Abhay Ashtekar

This is a brief overview of the current status of symmetry reduced models in Loop Quantum Gravity. The goal is to provide an introduction to other more specialized and detailed reviews that follow. Since most of this work is motivated by the physics of the very early universe, I will focus primarily on Loop Quantum Cosmology and discuss quantum aspects of black holes only briefly.


Author(s):  
Abhay Ashtekar ◽  
Brajesh Gupt ◽  
V. Sreenath

While the standard, six-parameter, spatially flat ΛCDM model has been highly successful, certain anomalies in the cosmic microwave background bring out a tension between this model and observations. The statistical significance of any one anomaly is small. However, taken together, the presence of two or more of them imply that according to standard inflationary theories we live in quite an exceptional Universe. We revisit the analysis of the PLANCK collaboration using loop quantum cosmology, where an unforeseen interplay between the ultraviolet and the infrared makes the primordial power spectrum scale dependent at very small k. Consequently, we are led to a somewhat different ΛCDM Universe in which anomalies associated with large scale power suppression and the lensing amplitude are both alleviated. The analysis also leads to new predictions for future observations. This article is addressed both to cosmology and loop quantum gravity communities, and we have attempted to make it self-contained.


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