Generalized uncertainty principle in Bianchi type I quantum cosmology

Abstract

We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

8 pages, 3 figures, to appear in PLB

References in corpus (37)

• Noncommutative Field Theory
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum Field Theory on Noncommutative Spaces
• Quantum gravity and minimum length
• Noncommutative Perturbative Dynamics
• Noncommutative Field Theory and Lorentz Violation
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• On Gravity and the Uncertainty Principle
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• UV/IR Relations in AdS Dynamics
• Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Signatures in the Planck Regime
• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
• Generalized Uncertainty Principle, Extra-dimensions and Holography
• Perturbation spectrum in inflation with cutoff
• Mode Generating Mechanism in Inflation with Cutoff
• Bounding Noncommutative QCD
• Noncommutative Quantum Cosmology
• Deconstructing de Sitter
• Minimal Length Uncertainty Relation and the Hydrogen Spectrum
• Some Aspects of Minimal Length Quantum Mechanics
• Trans-Planckian Effects in Inflationary Cosmology and the Modified Uncertainty Principle
• The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• Supersymmetric Noncommutative QED and Lorentz Violation
• Bianchi spacetimes in noncommutative phase-space
• Multidimensional Classical and Quantum Wormholes in Models with Cosmological Constant
• Dynamics of a magnetized Bianchi I universe with vacuum energy
• Planckian Scattering and Black Holes
• Nonpertubative Effects of Extreme Localization in Noncommutative Geometry

Cited by in corpus (37)

• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
• Quantum Black Hole in the Generalized Uncertainty Principle Framework
• A class of GUP solutions in deformed quantum mechanics
• 30 years in: Quo vadis generalized uncertainty principle?
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• Classical and Quantum Features of the Mixmaster Singularity
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
• Anisotropic Cosmological Model in Modified Brans--Dicke Theory
• Generalized Uncertainty Principle and the Ramsauer-Townsend Effect
• Harmonic oscillator with minimal length, minimal momentum, and maximal momentum uncertainties in SUSYQM framework
• Minimal Length and the Quantum Bouncer: A Nonperturbative Study
• Cosmology with minimal length uncertainty relations
• Einstein static universe from GUP
• Dark Energy within the Generalized Uncertainty Principle in Light of DESI DR2
• Dilaton cosmology and the Modified Uncertainty Principle
• Coherent States in Gravitational Quantum Mechanics
• The Mixmaster Universe in a generalized uncertainty principle framework
• Deformed phase space in a two dimensional minisuperspace model
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• Modified clock inequalities and modified black hole lifetime
• Constraints on Operator Ordering from Third Quantization
• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization
• Challenging $\Lambda$CDM with Higher-Order GUP Corrections
• The cosmological implications of a fundamental length: a DSR inspired de-Sitter spacetime
• Deformed spaces and loop cosmology
• Bianchi type I, Schutz perfect fluid and evolutionary quantum cosmology
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Signature Change by GUP
• Scalar field inflation driven by a modification of the Heisenberg algebra
• Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
• $\lambda {\varphi }^4$ Kink and sine-Gordon Soliton in the GUP Framework
• Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle