Loop quantum cosmology of k=1 FRW models

Abstract

The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the `difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.

Typos corrected. To appear in Physical Review D

References in corpus (27)

• Background Independent Quantum Gravity: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Absence of Singularity in Loop Quantum Cosmology
• Quantum Spin Dynamics (QSD)
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Quantum geometry and the Schwarzschild singularity
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Isotropic Loop Quantum Cosmology
• Graviton propagator from background-independent quantum gravity
• Effective Equations of Motion for Quantum Systems
• Homogeneous Loop Quantum Cosmology
• Quantum Observables and Recollapsing Dynamics
• Big Crunch Avoidance in k = 1 Semi-Classical Loop Quantum Cosmology
• On the Hamiltonian Constraint of Loop Quantum Cosmology
• Oscillatory Universes in Loop Quantum Cosmology and Initial Conditions for Inflation
• Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection
• On the regularization ambiguities in loop quantum gravity
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time
• An algebraic extension of Dirac quantization: Examples
• Observables and a Hilbert Space for Bianchi IX
• On the Physical Hilbert Space of Loop Quantum Cosmology
• Difficulties with Recollapsing models in Closed Isotropic Loop Quantum Cosmology
• Refined Algebraic Quantization in the oscillator representation of SL(2,R)
• Comments on the kinematical structure of loop quantum cosmology

Cited by in corpus (271)

• Loop Quantum Cosmology: A Status Report
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Minimal Length Scale Scenarios for Quantum Gravity
• Robustness of key features of loop quantum cosmology
• A new spinfoam vertex for quantum gravity
• Loop quantum cosmology of Bianchi I models
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• Planck stars
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Loop Quantum Dynamics of the Schwarzschild Interior
• Are loop quantum cosmos never singular?
• On the semiclassical limit of 4d spin foam models
• Space-Time Structure of Loop Quantum Black Hole
• 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
• Towards Spinfoam Cosmology
• Introduction to Loop Quantum Cosmology
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• Anti-deSitter universe dynamics in LQC
• Cosmological Models in Energy-Momentum-Squared Gravity
• Loop quantum cosmology of Bianchi type II models
• Is loop quantization in cosmology unique?
• Hybrid quantization of an inflationary universe
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Classical collapse to black holes and quantum bounces: A review
• Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$
• Quantum black holes in Loop Quantum Gravity
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Quantum field theory on a cosmological, quantum space-time
• Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
• Loop Quantization of Vacuum Bianchi I Cosmology
• Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Loop quantization of spherically symmetric midi-superspaces
• Quantum bounce and cosmic recall
• Positive cosmological constant in loop quantum cosmology
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Quantum cosmology with big-brake singularity
• Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology
• Shadow of a Naked Singularity without Photon Sphere
• Reissner-Nordström black holes in extended Palatini theories
• Exotic singularities and spatially curved Loop Quantum Cosmology
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
• The Einstein static universe in Loop Quantum Cosmology
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• The LQC evolution operator of FRW universe with positive cosmological constant
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Hybrid quantization of an inflationary model: The flat case
• Black Hole evaporation: A Perspective from Loop Quantum Gravity
• Super-inflation 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
• Dynamics of interacting phantom scalar field dark energy in Loop Quantum Cosmology
• Cosmological vector modes and quantum gravity effects
• Linearized dynamics from the 4-simplex Regge action
• Open FRW model in Loop Quantum Cosmology
• Testing loop quantum cosmology
• The gravitational wave background from super-inflation in 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
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• Numerical simulations of loop quantum Bianchi-I spacetimes
• Notes on dark energy interacting with dark matter and unparticle in loop quantum cosmology
• Coherent semiclassical states for loop quantum cosmology
• Prescriptions in Loop Quantum Cosmology: A comparative analysis
• On effective loop quantum geometry of Schwarzschild interior
• Exact solutions for Big Bounce in loop quantum cosmology
• Inflation with a Negative Cosmological Constant
• Quantum Cosmology: Effective Theory
• Properties of the Volume Operator in Loop Quantum Gravity I: Results
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• Warm inflationary model in loop quantum cosmology
• Investigating Loop Quantum Gravity with EHT Observational Effects of Rotating Black holes
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Bouncing compact objects I: Quantum extension of the Oppenheimer-Snyder collapse
• Thermal fluctuations in loop cosmology
• On the Semiclassical Limit of Loop Quantum Cosmology
• Dynamics for a 2-vertex Quantum Gravity Model
• Primordial black holes in loop quantum cosmology: The effect on the threshold
• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
• The Evolution of $\Lambda$ Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
• Generalized effective description of loop quantum cosmology
• The covariant entropy bound and loop quantum cosmology
• Properties of the spherically symmetric polymer black holes
• Complete, Single-Horizon Quantum Corrected Black Hole Spacetime
• Lattice Refining Loop Quantum Cosmology and Inflation
• The cosmological BCS mechanism and the Big Bang Singularity
• Numerical loop quantum cosmology: an overview
• The flat FRW model in LQC: the self-adjointness
• Stability of the Einstein Static Universe in open cosmological models
• Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology
• Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
• Lattice loop quantum cosmology: scalar perturbations
• Physical time and other conceptual issues of QG on the example of LQC
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Singularities in loop quantum cosmology
• Numerical evidence of regularized correlations in spin foam gravity
• Group field cosmology: a cosmological field theory of quantum geometry
• Primordial power spectrum from the Dapor-Liegener model of loop quantum cosmology
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• Inflation in the closed FLRW model and the CMB
• Polymer quantization, singularity resolution and the 1/r^2 potential
• General dissipative coefficient in warm intermediate inflation in loop quantum cosmology in light of Planck and BICEP2
• On the Onset of Inflation in Loop Quantum Cosmology
• Loop Quantum Gravity
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Bouncing Unitary Cosmology I: Mini-Superspace General Solution
• Cosmological Hysteresis and the Cyclic Universe
• An Overview on the Nature of the Bounce in LQC and PQM
• Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
• Modified gravity in Arnowitt-Deser-Misner formalism
• Wiggles in the cosmic microwave background radiation: echoes from non-singular cyclic-inflation
• Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
• Classical Setting and Effective Dynamics for Spinfoam Cosmology
• Loop Quantum Cosmology: A brief review
• Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology
• Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
• Observational constraints of a power spectrum from super-inflation in Loop Quantum Cosmology
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Loop Quantum Cosmology corrections to inflationary models
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Transcending Big Bang in Loop Quantum Cosmology: Recent Advances
• Quantum gravity on a square graph
• Group theoretical Quantization of Isotropic Loop Cosmology
• Loop Quantum Cosmology: A cosmological theory with a view
• Extended Phase Space Analysis of Interacting Dark Energy Models in Loop Quantum Cosmology
• Emergent universe in theories with natural UV cutoffs
• Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies
• Cyclic Inflation
• Recollapsing quantum cosmologies and the question of entropy
• Effective dynamics of the hybrid quantization of the Gowdy T^3 universe
• Fermions in Loop Quantum Cosmology and the Role of Parity
• Brief review on black hole loop quantization
• Effective constrained polymeric theories and their continuum limit
• The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of Loop Quantum Cosmology
• Some conceptual issues in loop quantum cosmology
• Loop quantum cosmology with higher order holonomy corrections
• Generalized modified gravity with the second order acceleration equation
• Numerical Techniques in Loop Quantum Cosmology
• Graceful exit via polymerization of pre-big bang cosmology
• Quantum Riemannian geometry and particle creation on the integer line
• Emergence of spacetime dynamics in entropy corrected and braneworld models
• Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
• Chimera: A hybrid approach to numerical loop quantum cosmology
• Inverse volume corrections to emergent tachyonic inflation in loop quantum cosmology
• Non-singular bounce transitions in the multiverse
• Bianchi-I cosmological model and crossing singularities
• The high-density regime of kinetic-dominated loop quantum cosmology
• Inflation from non-minimally coupled scalar field in loop quantum cosmology
• Tensor perturbations during inflation in a spatially closed Universe
• Einstein-Cartan gravitational collapse of a homogeneous Weyssenhoff fluid
• Non-singular AdS-dS transitions in a landscape scenario
• Loop quantum cosmology with self-dual variables
• Singularity avoidance in the hybrid quantization of the Gowdy model
• The region interior to the event horizon of the Regular Hayward Black Hole
• Learning about Quantum Gravity with a Couple of Nodes
• Unimodular Loop Quantum Cosmology
• Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme
• Observations on interfacing loop quantum gravity with cosmology
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• How loopy is the quantum bounce? A heuristic analysis of higher order holonomy corrections in LQC
• Phase space analysis of the bouncing universe with stringy effects
• The no-boundary wave function for loop quantum cosmology
• Quantum gravitational onset of Starobinsky inflation in a closed universe
• Loop Quantum Cosmology
• Polymer quantization of the Einstein-Rosen wormhole throat
• Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
• Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections
• Loop Quantum Gravity motivated multihorizon rotating black holes
• Revisiting quantum black holes from effective loop quantum gravity
• Singularity resolution from polymer quantum matter
• Separable Hilbert space for loop quantization
• Quantum Gravity, Time, Bounces and Matter
• The Big Bang and the Quantum
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Effective dynamics of the closed loop quantum cosmology
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• Improved dynamics and gravitational collapse of tachyon field coupled with a barotropic fluid
• Loop quantum cosmology and singularities
• Anisotropic loop quantum cosmology with self-dual variables
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Singularity avoidance and time in quantum gravity
• Bouncing universe from a modified dispersion relation
• Big Bang Singularity Resolution In Quantum Cosmology
• 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
• Hysteresis and beats in loop quantum cosmology
• Quantum gravity on polygons and $\mathbb{R}\times {\mathbb{Z}}_n$ FLRW model
• Higher curvature counter terms cause the bounce in loop cosmology
• Gravitational Particle Production in Loop Quantum Cosmology
• Canonical wave packets in quantum cosmology
• Loop Quantum Cosmology: Effective theories and oscillating universes
• Fuzzy and discrete black hole models
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum dynamics of the Einstein-Rosen wormhole throat
• Hysteresis in the Sky
• Vector fields and Loop Quantum Cosmology
• Quantum gravity might restrict a cyclic evolution
• Dynamical eigenfunctions and critical density in loop quantum cosmology
• Gravitational Particle Production and the Validity of Effective Descriptions in Loop Quantum Cosmology
• Tunneling wavefunction proposal with loop quantum geometry effects
• The quantum effect on Friedmann equation in FRW universe
• Semiclassical solutions of generalized Wheeler-DeWitt cosmology
• Holography from loop quantum gravity
• Measuring the last burst of non-singular black holes
• The volume operator in loop quantum cosmology
• Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity
• Cosmological inflation driven by holonomy corrections of loop quantum cosmology
• The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology
• Friedmann equations and cosmic bounce in a modified cosmological scenario
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Is the diagonal case a general picture for Loop Quantum Cosmology?
• Stellar collapse with pressure in effective loop quantum gravity
• Universe from vacuum in loop-string cosmology
• From loop quantum gravity to cosmology: the two-vertex model
• Dark matter as the Bose-Einstein condensation in loop quantum cosmology
• Solvable Loop Quantum Cosmology: domain of the volume observable and semiclassical states
• Alternative $k=-1$ loop quantum cosmology
• Quantum Riemannian geometry of the discrete interval and q-deformation
• Non-singular flat universes in braneworld and Loop Quantum Cosmology
• Cosmological perturbations with inverse-volume corrections in loop quantum cosmology
• Lessons from gauge fixing and polymerization of loop quantum black holes with a cosmological constant
• Geometric phases and cyclic isotropic cosmologies
• Power spectrum and anisotropy of super inflation in loop quantum cosmology
• The generalized second law of thermodynamics of the universe bounded by the event horizon and modified gravity theories
• Discretisation parameter and operator ordering in loop quantum cosmology with the cosmological constant
• Schrödinger-like quantum dynamics in loop quantized black holes
• Quantum Space-times: Beyond the Continuum of Minkowski and Einstein
• U(N) invariant dynamics for a simplified Loop Quantum Gravity model
• Quantum gravitational non-singular tunneling wavefunction proposal
• Quantum vacuum effects on the final fate of a collapsing ball of dust
• Singularity Resolution in Isotropic Loop Quantum Cosmology: Recent Developments
• Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations
• Effective equations of motion for constrained quantum systems: A study of the Bianchi I loop quantum cosmology
• Dark Energy as a Relic of the Vacuum-Energy Cancellation?
• Universe's memory and spontaneous coherence in loop quantum cosmology
• Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace
• Loop Quantum Cosmology and the Fine Structure Constant
• On the role of dissipative effects in the quantum gravitational onset of warm Starobinsky inflation in a closed universe
• Non-singular Universes a la Palatini
• Asymmetric cyclic evolution in polymerised cosmology
• Non-singular non-flat universes
• Loop quantum gravity and observations
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• Basis Function Method for Numerical Loop Quantum Cosmology: The Schwarzschild Black Hole Interior
• Conserved quantities in isotropic loop quantum cosmology
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Does loop quantum ${\mu }_o$ scheme permit a black hole formation?
• Unitary evolution and cosmic acceleration in Loop Quantum Cosmology