Loop quantum cosmology of Bianchi type IX models

Abstract

The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.

20 pages

References in corpus (31)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Loop Quantum Cosmology: An Overview
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Is loop quantization in cosmology unique?
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Loop Quantization of Vacuum Bianchi I Cosmology
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Barbero-Immirzi field in canonical formalism of pure gravity
• Dynamical coherent states and physical solutions of quantum cosmological bounces
• Stepping out of Homogeneity in Loop Quantum Cosmology
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Cosmological footprints of loop quantum gravity
• The Bianchi IX model in Loop Quantum Cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• Open FRW model in Loop Quantum Cosmology
• The gravitational wave background from super-inflation in Loop Quantum Cosmology
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• The flat FRW model in LQC: the self-adjointness
• Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture
• Fermions in Loop Quantum Cosmology and the Role of Parity

Cited by in corpus (128)

• Loop Quantum Cosmology: A Status Report
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
• Homogeneous cosmologies as group field theory condensates
• Probability of Inflation in Loop Quantum Cosmology
• Anisotropic Universe Models in f(T) Gravity
• Introduction to Loop Quantum Cosmology
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
• Hybrid quantization of an inflationary model: The flat case
• Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
• Contrasting features of anisotropic loop quantum cosmologies: the role of spatial curvature
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Testing loop quantum cosmology
• Loop quantum cosmology of k=1 FRW: A tale of two bounces
• Phenomenological investigation of a quantum gravity extension of inflation with the Starobinsky potential
• A Hamiltonian Formulation of the BKL Conjecture
• Numerical simulations of loop quantum Bianchi-I spacetimes
• Coherent semiclassical states for loop quantum cosmology
• Prescriptions in Loop Quantum Cosmology: A comparative analysis
• Unitarity, clock dependence and quantum recollapse in quantum cosmology
• Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization
• On effective loop quantum geometry of Schwarzschild interior
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• Generalized effective description of loop quantum cosmology
• The loop quantum cosmology bounce as a Kasner transition
• Numerical loop quantum cosmology: an overview
• Lattice loop quantum cosmology: scalar perturbations
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Preinflationary dynamics in loop quantum cosmology: Monodromy Potential
• Primordial power spectrum from the Dapor-Liegener model of loop quantum cosmology
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• Loop Quantum Gravity
• Smooth Quantum Dynamics of Mixmaster Universe
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• A quantum gravitational inflationary scenario in Bianchi-I spacetime
• Singularity avoidance in a quantum model of the Mixmaster universe
• A quantum reduction to Bianchi I models in loop quantum gravity
• An Overview on the Nature of the Bounce in LQC and PQM
• Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Loop Quantum Cosmology: A brief review
• Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
• Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
• A Homogeneous Model of Spinfoam Cosmology
• Loop Quantum Cosmology: A cosmological theory with a view
• The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of Loop Quantum Cosmology
• Numerical Techniques in Loop Quantum Cosmology
• Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
• Vertex Expansion for the Bianchi I model
• Loop quantum cosmology with self-dual variables
• New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
• Non-singular AdS-dS transitions in a landscape scenario
• Non-singular Brans-Dicke collapse in deformed phase space
• Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
• Learning about Quantum Gravity with a Couple of Nodes
• Singularity avoidance in the hybrid quantization of the Gowdy model
• Polymer representation of the Bianchi IX Cosmology in the Misner variables
• Unimodular Loop Quantum Cosmology
• Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• Loop Quantum Cosmology
• Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections
• The Big Bang and the Quantum
• Unavoidable shear from quantum fluctuations in contracting cosmologies
• Singularity resolution from polymer quantum matter
• A critical analysis of the cosmological implementation of Loop Quantum Gravity
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Polymer dynamics of isotropic universe in Ashtekar and in volume variables
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• Anisotropic Spinfoam Cosmology
• Anisotropic loop quantum cosmology with self-dual variables
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• A quantum gravity extension to the Mixmaster dynamics
• Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
• Minimal Coupling and Attractors
• Bianchi type-I string cosmological model in the presence of a magnetic field: classical versus loop quantum cosmology approaches
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach
• New class of exact solutions to Einstein-Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry
• Open problems in mathematical physics
• Discrete spectrum of the quantum Reissner - Nordström geometry
• Quantum cosmology of pure connection general relativity
• Friedmann equations and cosmic bounce in a modified cosmological scenario
• Quantum cosmology of Bianchi VIII, IX LRS geometries
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Cyclic universe from Loop Quantum Gravity
• Solvable Loop Quantum Cosmology: domain of the volume observable and semiclassical states
• Matter in Loop Quantum Gravity
• Path Integral of Bianchi I models in Loop Quantum Cosmology
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Fate of Mixmaster Chaos in a Deformed Algebra framework
• Quantum theory of the Bianchi II model
• Loop Quantum Gravity and the The Planck Regime of Cosmology
• Lectures on LQG/LQC
• Magnetic Bianchi type II string cosmological model in loop quantum cosmology
• Taming Fluctuations for Gaussian States in Loop Quantum Cosmology
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Loop Quantum Cosmology and the Fine Structure Constant
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Thermodynamics of spacetime from minimal area
• Crossing the singularity of a gravitational wave collision
• Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models
• Loop Quantum Cosmology: Anisotropy and singularity resolution
• Semiclassical study of the Mixmaster model: the quantum Kasner map