Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology

Abstract

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.

34 pages, v2: minor changes

References in corpus (13)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Are loop quantum cosmos never singular?
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Quantum bounce and cosmic recall
• Why are the effective equations of loop quantum cosmology so accurate?
• The Bianchi IX model in Loop Quantum Cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• Physical time and other conceptual issues of QG on the example of LQC
• Holonomy Operator and Quantization Ambiguities on Spinor Space

Cited by in corpus (56)

• From black holes to white holes: a quantum gravitational, symmetric bounce
• Cosmological Models in Energy-Momentum-Squared Gravity
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Why are the effective equations of loop quantum cosmology so accurate?
• Black hole collapse and bounce in effective loop quantum gravity
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• On the fate of quantum black holes
• Hybrid loop quantum cosmology and predictions for the cosmic microwave background
• Testing loop quantum cosmology
• Numerical simulations of loop quantum Bianchi-I spacetimes
• 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
• Emergence of product of constant curvature spaces in loop quantum cosmology
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• The loop quantum cosmology bounce as a Kasner transition
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Preinflationary dynamics in loop quantum cosmology: Monodromy Potential
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Loop Quantum Cosmology: A brief review
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Status of Birkhoff's theorem in polymerized semiclassical regime of Loop Quantum Gravity
• The constraint algebra in Smolins' $G\to 0$ limit of 4d Euclidean Gravity
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
• New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
• Loop quantum cosmology with self-dual variables
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Primordial power spectrum from a matter-Ekpyrotic bounce scenario in loop quantum cosmology
• The sounds of science: a symphony for many instruments and voices
• Loop quantum cosmology: relation between theory and observations
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Anisotropic loop quantum cosmology with self-dual variables
• Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology
• A quantum gravity extension to the Mixmaster dynamics
• Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
• Open problems in mathematical physics
• The landscape of polymer quantum cosmology
• Quantum gravity might restrict a cyclic evolution
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Stellar collapse with pressure in effective loop quantum gravity
• Ambiguous power spectrum from a quantum bounce
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• 2+1 dimensional loop quantum cosmology of Bianchi I models
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology