Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I

Abstract

We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time. In order to retrieve the system dynamics when no such a suitable clock field is present, we explore different constructions of families of unitarily related partial observables. These observables are parameterized, respectively, by: (i) one of the components of the densitized triad, and (ii) its conjugate momentum; each of them playing the role of an evolution parameter. Exploiting the properties of the considered example, we investigate in detail the domains of applicability of each construction. In both cases the observables possess a neat physical interpretation only in an approximate sense. However, whereas in case (i) such interpretation is reasonably accurate only for a portion of the evolution of the universe, in case (ii) it remains so during all the evolution (at least in the physically interesting cases). The constructed families of observables are next used to describe the evolution of the Bianchi I universe. The performed analysis confirms the robustness of the bounces, also in absence of matter fields, as well as the preservation of the semiclassicality through them. The concept of evolution studied here and the presented construction of observables are applicable to a wide class of models in LQC, including quantizations of the Bianchi I model obtained with other prescriptions for the improved dynamics.

RevTex4, 22 pages, 4 figures

References in corpus (41)

• Background Independent Quantum Gravity: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Robustness of key features of loop quantum cosmology
• Partial observables
• Loop quantum cosmology of k=1 FRW models
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Loop quantum cosmology of Bianchi I models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Partial and Complete Observables for Canonical General Relativity
• Are loop quantum cosmos never singular?
• Non-Singular Bouncing Universes in Loop Quantum Cosmology
• Loop Quantum Cosmology: An Overview
• Homogeneous Loop Quantum Cosmology
• Loop quantum cosmology and the k = - 1 RW model
• Black holes in loop quantum gravity: the complete space-time
• Quantum Observables and Recollapsing Dynamics
• 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?
• Reduced Phase Space Quantization and Dirac Observables
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Covariant Effective Action for Loop Quantum Cosmology a la Palatini
• Loop Quantization of Vacuum Bianchi I Cosmology
• Semi-classical States, Effective Dynamics and Classical Emergence in Loop Quantum Cosmology
• Quantum bounce and cosmic recall
• 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
• Cosmological footprints of loop quantum gravity
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time
• Open FRW model in Loop Quantum Cosmology
• Observables and a Hilbert Space for Bianchi IX
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• High-order gauge-invariant perturbations of a spherical spacetime
• The flat FRW model in LQC: the self-adjointness
• Physical time and other conceptual issues of QG on the example of LQC
• Loop Quantum Cosmology corrections to inflationary models
• Non-Perturbative Canonical Quantization of Minisuperspace Models: Bianchi Types I and II

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• Loop Quantum Cosmology: A Status Report
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• Problem of Time in Quantum Gravity
• An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Introduction to Loop Quantum Cosmology
• Hybrid quantization of an inflationary universe
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• Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology
• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
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• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity
• The LQC evolution operator of FRW universe with positive cosmological constant
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• Hybrid quantization of an inflationary model: The flat case
• Contrasting features of anisotropic loop quantum cosmologies: the role of spatial curvature
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Effective relational dynamics of a nonintegrable cosmological model
• Phenomenological investigation of a quantum gravity extension of inflation with the Starobinsky potential
• Numerical simulations of loop quantum Bianchi-I spacetimes
• On effective loop quantum geometry of Schwarzschild interior
• Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization
• Emergence of product of constant curvature spaces in loop quantum cosmology
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• The loop quantum cosmology bounce as a Kasner transition
• Hybrid Loop Quantum Cosmology: An Overview
• Numerical loop quantum cosmology: an overview
• Primordial tensor modes of the early Universe
• Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
• A relational Hamiltonian for group field theory
• Preinflationary dynamics in loop quantum cosmology: Monodromy Potential
• Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology
• Loop Quantum Gravity
• A quantum gravitational inflationary scenario in Bianchi-I spacetime
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Glimpses of Space-Time Beyond the Singularities Using Supercomputers
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Is classical flat Kasner spacetime flat in quantum gravity?
• Effective dynamics of the hybrid quantization of the Gowdy T^3 universe
• Brief review on black hole loop quantization
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• Exhaustive investigation of the duration of inflation in effective anisotropic loop quantum cosmology
• Numerical Techniques in Loop Quantum Cosmology
• Bianchi-I cosmological model and crossing singularities
• Non-singular AdS-dS transitions in a landscape scenario
• Loop quantization of the Gowdy model with local rotational symmetry
• Singularity avoidance in the hybrid quantization of the Gowdy model
• Observational consequences of Bianchi I spacetimes in loop quantum cosmology
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Observations on interfacing loop quantum gravity with cosmology
• Loop Quantum Cosmology
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology
• Anisotropic loop quantum cosmology with self-dual variables
• Modified Friedmann equation and survey of solutions in effective Bianchi-I loop quantum cosmology
• Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries
• A quantum gravity extension to the Mixmaster dynamics
• Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics
• Chaos, Dirac observables and constraint quantization
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
• Vector fields and Loop Quantum Cosmology
• Dapor-Liegener formalism of loop quantum cosmology for Bianchi I spacetimes
• A path-integral approach to the problem of time
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Evolution in totally constrained models: Schrödinger vs. Heisenberg pictures
• Time evolution in quantum cosmology
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Freeze-free cosmological evolution with a non-monotonic internal clock
• Schrödinger-like quantum dynamics in loop quantized black holes
• 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
• Phenomenology of loop quantum cosmology
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• Expansion-sensitive coupling of a local quantum system in de Sitter cosmology