Dilaton cosmology, noncommutativity, and generalized uncertainty principle

2008/01/31 by Babak Vakili · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.77.044023

published as Phys.Rev.D77:044023,2008 · 16 pages, 3 figures, typos corrected

openalex publication_date 2008/02/14 · arxiv created 2008/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between the minisuperspace variables and their momenta operators. I extend these deformed commutating relations to the corresponding deformed Poisson algebra. For an exponential dilaton potential, the exact classical and quantum solutions in the commutative and noncommutative cases, and some approximate analytical solutions in the case of GUP, are presented and compared.

Citations

• Classical Implications of the Minimal Length Uncertainty Relation
• Star Operation in Quantum Mechanics
• Graceful exit in quantum string cosmology
• Maximal localization in the presence of minimal uncertainties in positions and in momenta
• Supersymmetric noncommutative QED and Lorentz violation
• INFLATION, DEFLATION, AND FRAME-INDEPENDENCE IN STRING COSMOLOGY
• Bianchi spacetimes in noncommutative phase space
• Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Mtheory as a matrix model: A conjecture
• Noncommutative quantum mechanics
• Noncommutative Cosmology

Cited by

• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization