Stability analysis of Einstein’s universe in loop quantum cosmology

2020 ◽  
Vol 35 (28) ◽  
pp. 2050166
Author(s):  
Eamon Mc Caughey
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Hamiltonian Structure ◽  
Loop Quantum Cosmology ◽  
Universe Model ◽  
Integrals Of Motion ◽  
Cyclic Universe ◽  
The Stability

A stability analysis of Einstein’s universe in both classical general relativity and semiclassical loop quantum cosmology regimes is presented. The stability properties of the general relativity model are significantly altered due to loop quantum gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The loop quantum cosmology solutions are restricted to an open universe model [Formula: see text] and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

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 THE DYNAMICS OF TACHYON FIELD WITH AN INVERSE SQUARE POTENTIAL IN LOOP QUANTUM COSMOLOGY

2013 ◽  
Vol 22 (06) ◽  
pp. 1350030 ◽  
Author(s):  
FEI HUANG ◽  
JIAN-YANG ZHU ◽  
KUI XIAO
Keyword(s):  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Phase Plane Analysis ◽  
Late Time ◽  
Stable Node ◽  
Time Behavior ◽  
Tachyon Field ◽  
Plane Analysis ◽  
The Stability

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late-time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index 0 < γ < 2 is added and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.

scholarly journals CYCLIC UNIVERSE WITH QUINTOM MATTER IN LOOP QUANTUM COSMOLOGY

2009 ◽  
Vol 24 (15) ◽  
pp. 1237-1246 ◽  
Author(s):  
HUA-HUI XIONG ◽  
TAOTAO QIU ◽  
YI-FU CAI ◽  
XINMIN ZHANG
Keyword(s):  
Scalar Field ◽  
Quantum Cosmology ◽  
Model Building ◽  
Numerical Calculations ◽  
Loop Quantum Cosmology ◽  
Cyclic Universe

In this paper, we study the possibility of model building of cyclic universe with Quintom matter in the framework of Loop Quantum Cosmology. After a general demonstration, we provide two examples, one with double-fluid and another double-scalar field, to show how such a scenario is obtained. Analytical and numerical calculations are both presented in the paper.

scholarly journals Beyond General Relativity: Models for Quantum Gravity, Loop Quantum Cosmology and Black Holes

Universe ◽  
2020 ◽  
Vol 6 (12) ◽  
pp. 232
Author(s):  
Nick E. Mavromatos
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Precision Measurements ◽  
Loop Quantum Cosmology ◽  
The Past

In the past two decades, we have witnessed extraordinary progress in precision measurements in 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 Some conceptual issues in loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642008 ◽  
Author(s):  
Aurélien Barrau ◽  
Boris Bolliet
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Symmetry Reduction ◽  
Loop Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Quantum Spacetime ◽  
Open Issues

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.

scholarly journals Loop quantum gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1530005 ◽  
Author(s):  
Dah-Wei Chiou
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Black Hole Thermodynamics ◽  
Loop Quantum Cosmology ◽  
General Picture ◽  
Orderly Fashion ◽  
Introductory Review ◽  
Open Issues

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.

scholarly journals Deformation quantization and the tomographic representation of quantum fields

2020 ◽  
Vol 17 (14) ◽  
pp. 2050217
Author(s):  
Jasel Berra-Montiel ◽  
Roberto Cartas-Fuentevilla
Keyword(s):  
Quantum Cosmology ◽  
Deformation Quantization ◽  
Loop Quantum Gravity ◽  
Star Product ◽  
Functional Integral ◽  
Loop Quantum Cosmology ◽  
Quantum Fields ◽  
Quantization Formalism ◽  
Tomographic Representation ◽  
Functional Integral Representation

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.

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