Loop quantum cosmology of Bianchi I models

Abstract

The "improved dynamics" of loop quantum cosmology is extended to include anisotropies of the Bianchi I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is non-trivial because one has to face several conceptual subtleties as well as technical difficulties. These include: a better understanding of the relation between loop quantum gravity (LQG) and loop quantum cosmology (LQC); handling novel features associated with the non-local field strength operator in presence of anisotropies; and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz (BKL) conjecture on the nature of generic space-like singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic space-like singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down \emph{exactly} to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of LQG to that of LQC.

33 pages, 2 figures

References in corpus (27)

• 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
• Loop quantum cosmology of Bianchi type IX models
• 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?
• Loop quantum cosmology and inhomogeneities
• 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
• Dynamical coherent states and physical solutions of quantum cosmological bounces
• Barbero-Immirzi field in canonical formalism of pure gravity
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• 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
• Numerical solutions to lattice-refined models in loop quantum cosmology

Cited by in corpus (230)

• 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
• Loop quantum cosmology of Bianchi type IX models
• Probability of Inflation in Loop Quantum Cosmology
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Introduction to Loop Quantum Cosmology
• Loop quantum cosmology of Bianchi type II models
• Loop quantum cosmology and slow roll inflation
• Hybrid quantization of an inflationary universe
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Quantum field theory on a cosmological, quantum space-time
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Bouncing cosmologies from quantum gravity condensates
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology
• Exotic singularities and spatially curved Loop Quantum Cosmology
• Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
• Quantum-Reduced Loop Gravity: Cosmology
• Observational issues in loop quantum cosmology
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• 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
• Quantum Gravity in the Sky: Interplay between fundamental theory and observations
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition
• 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
• Numerical simulations of loop quantum Bianchi-I spacetimes
• A Hamiltonian Formulation of the BKL Conjecture
• Prescriptions in Loop Quantum Cosmology: A comparative analysis
• Coherent semiclassical states for loop 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
• Emergence of a low spin phase in group field theory condensates
• Inflationary observables in loop quantum cosmology
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Nonsingular bouncing cosmologies in light of BICEP2
• Quantum Reduced Loop Gravity: Semiclassical limit
• Generalized effective description of loop quantum cosmology
• The loop quantum cosmology bounce as a Kasner transition
• Hybrid Loop Quantum Cosmology: An Overview
• Numerical loop quantum cosmology: an overview
• Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology
• On Singular Semi-Riemannian Manifolds
• Lattice loop quantum cosmology: scalar perturbations
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi-I universe with different inflaton potentials and initial conditions
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Primordial power spectrum from the Dapor-Liegener model of loop quantum cosmology
• Preinflationary dynamics in loop quantum cosmology: Monodromy Potential
• Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• A spin-foam vertex amplitude with the correct semiclassical limit
• Loop Quantum Gravity
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• A quantum gravitational inflationary scenario in Bianchi-I spacetime
• A quantum reduction to Bianchi I models in loop quantum gravity
• Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
• An Overview on the Nature of the Bounce in LQC and PQM
• Quantum Reduced Loop Gravity: a realistic Universe
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology
• Local spinfoam expansion in loop quantum cosmology
• Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
• Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
• Hybrid Models in Loop Quantum Cosmology
• Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology
• Consistent probabilities in loop quantum cosmology
• On the Uniqueness of Kinematics of Loop Quantum Cosmology
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Classical and quantum cosmology of Born-Infeld type models
• A Homogeneous Model of Spinfoam Cosmology
• Loop Quantum Cosmology: A cosmological theory with a view
• Echo of the Quantum Bounce
• Group theoretical Quantization of Isotropic Loop Cosmology
• Effective dynamics of the hybrid quantization of the Gowdy T^3 universe
• Is classical flat Kasner spacetime flat in quantum gravity?
• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang singularity
• An embedding of loop quantum cosmology in (b, v) variables into a full theory context
• The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of Loop Quantum Cosmology
• Numerical Techniques in Loop Quantum Cosmology
• Chimera: A hybrid approach to numerical loop quantum cosmology
• The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity
• Symmetry Reduction of Loop Quantum Gravity
• Exhaustive investigation of the duration of inflation in effective anisotropic loop quantum cosmology
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Vertex Expansion for the Bianchi I model
• Uniqueness of the Representation in Homogeneous Isotropic LQC
• Non-singular AdS-dS transitions in a landscape scenario
• Loop quantization of the Gowdy model with local rotational symmetry
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Interpretation of the triad orientations in loop quantum cosmology
• Predictions for the CMB from an anisotropic quantum bounce
• Observational consequences of Bianchi I spacetimes in loop quantum cosmology
• Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
• Is limiting curvature mimetic gravity an effective polymer quantum gravity?
• Singularity avoidance in the hybrid quantization of the Gowdy model
• Observations on interfacing loop quantum gravity with cosmology
• Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme
• Loop quantum cosmology of the Bianchi I model: complete quantization
• Unimodular Loop Quantum Cosmology
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved
• Loop Quantum Cosmology
• Hamiltonian theory of classical and quantum gauge invariant perturbations in Bianchi I spacetimes
• Embedding loop quantum cosmology without piecewise linearity
• Singularity resolution from polymer quantum matter
• The Big Bang and the Quantum
• Unavoidable shear from quantum fluctuations in contracting cosmologies
• Diffeomorphism invariant cosmological symmetry in full quantum gravity
• The sounds of science: a symphony for many instruments and voices
• Polymer dynamics of isotropic universe in Ashtekar and in volume variables
• A critical analysis of the cosmological implementation of Loop Quantum Gravity
• Loop quantum cosmology: relation between theory and observations
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Bianchi I model in terms of nonstandard loop quantum cosmology: Classical dynamics
• Anisotropic Spinfoam Cosmology
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology
• Unstable Anisotropic Loop Quantum Cosmology
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Anisotropic loop quantum cosmology with self-dual variables
• Modified Friedmann equation and survey of solutions in effective Bianchi-I loop quantum cosmology
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• A Quantum Complete Prelude to Inflation
• Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries
• Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
• State refinements and coarse graining in a full theory embedding of loop quantum cosmology
• Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model
• Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime
• A quantum gravity extension to the Mixmaster dynamics
• Minimal Coupling and Attractors
• Big Bang Singularity Resolution In Quantum Cosmology
• Deriving loop quantum cosmology dynamics from diffeomorphism invariance
• Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes
• Seeing through the cosmological bounce: Footprints of the contracting phase and luminosity distance in bouncing models
• Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Cosmic anisotropy with Reduced Relativistic Gas
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
• n-dimensional non-commutative GUP quantization and application to the Bianchi I model
• Singular General Relativity
• Towards anisotropic cosmology in group field theory
• Vector fields and Loop Quantum Cosmology
• Dynamical eigenfunctions and critical density in loop quantum cosmology
• Discrete spectrum of the quantum Reissner - Nordström geometry
• Observational constraints on anisotropies for bouncing alternatives to inflation
• Dapor-Liegener formalism of loop quantum cosmology for Bianchi I spacetimes
• Quantum cosmology of Bianchi VIII, IX LRS geometries
• Bianchi type I, Schutz perfect fluid and evolutionary quantum cosmology
• Loop Quantum Cosmology of non-diagonal Bianchi models
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Is the diagonal case a general picture for Loop Quantum Cosmology?
• Universal scattering laws for quiescent bouncing cosmology
• Solvable Loop Quantum Cosmology: domain of the volume observable and semiclassical states
• Matter in Loop Quantum Gravity
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
• Cyclic universe from Loop Quantum Gravity
• Bianchi I effective dynamics in Quantum Reduced Loop Gravity
• Lattice Refining Loop Quantum Cosmology from an Isotropic Embedding of Anisotropic Cosmology
• Variety of $(d+1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce
• Loop Quantum Gravity and the The Planck Regime of Cosmology
• Path Integral of Bianchi I models in Loop Quantum Cosmology
• Quantum theory of the Bianchi II model
• Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
• Discretisation parameter and operator ordering in loop quantum cosmology with the cosmological constant
• Lectures on LQG/LQC
• Critical Insight into the Cosmological Sector of Loop Quantum Gravity
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• A Class of LQC--inspired Models for Homogeneous, Anisotropic Cosmology in Higher Dimensional Early Universe
• Magnetic Bianchi type II string cosmological model in loop quantum cosmology
• Quantum isotropy and the reduction of dynamics in Bianchi I
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models
• Phenomenology of loop quantum cosmology
• Loop Quantum Cosmology and the Fine Structure Constant
• Classical bouncing Universes from vector fields
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory
• Universe's memory and spontaneous coherence in loop quantum cosmology
• Cosmological implications of the hydrodynamical phase of group field theory
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections
• Inhomogenous loop quantum cosmology with matter
• Isotropic LQC and LQC--inspired Models with a massless scalar field as Generalised Brans--Dicke theories
• LQ Stars : Modifying the Tolman -- Oppenheimer -- Volkoff equations a la LQC
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• Cosmology in Loop Quantum Gravity: symmetry reduction preserving gauge degrees of freedom
• Loop quantum gravity and observations
• Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions
• On the dynamics of single-vertex states in quantum-reduced loop gravity
• Quantum Gowdy model within the new loop quantum cosmology improved dynamics
• Thermodynamics of spacetime from minimal area
• Black hole or Fuzz ball or a Loop quantum star ? Assessing the fate of a massive collapsing star
• Loop Quantum Cosmology of Bianchi I Model in $\bar{\mu }$ and ${\bar{\mu }}^{\prime }$ Schemes with Higher Order Holonomy Corrections
• A Twisted ${\mathcal{C}}^{\star }$-algebra formulation of Quantum Cosmology with application to the Bianchi I model
• Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models
• 2+1 dimensional loop quantum cosmology of Bianchi I models
• Analysis of efficiency limiting processes in thin film Cu(In,Ga)(S,Se)2 electrodeposited solar cells
• Quantum geometrical current and coherence of the open gravitation system: loop quantum gravity coupled with a thermal scalar field
• Conserved quantities in isotropic loop quantum cosmology
• Loop Quantum Cosmology: Anisotropy and singularity resolution
• Examination of the nature of the Bianchi type cosmological singularities
• Expansion-sensitive coupling of a local quantum system in de Sitter cosmology
• Degenerate Limits of Scalar-Tensor Gravity
• Crossing the singularity of a gravitational wave collision
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP