Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms

Abstract

We compare in some detail Polymer Quantum Mechanics and the Generalized Uncertainty Principle approach to clarify to what extent we can treat them on the same footing. We show that, while on a semiclassical level they may be formulated as similar modifications of the Poisson algebra, on a quantum level they intrinsically differ because PQM implies no absolute minimal uncertainty on position. Then we implement these schemes to Bianchi I cosmology on a semiclassical level deforming only the algebra of the Universe volume, searching for alternative formulations able to account for the modified Friedmann equations emerging in Brane Cosmology and Loop Quantum Cosmology. On a pure quantum level, we implement the two approaches through their original setups and reduce the two resulting Wheeler-DeWitt equations to the same morphological structure, showing how the polymer formalism is associated with a bouncing dynamics while in the Generalized Uncertainty Principle case the singularity is still present. The implications of the wavepacket spreading are also discussed in both approaches, outlining that, when the singularity survives, the Planckian era must necessarily be approached by a fully quantum (non-peaked) state of the Universe.

23 pages, 6 figures. Invited contribution to IJGMMP special issue for the conference "Geometric Foundations of Gravity 2021" (Tartu, Estonia, June 28-July 2, 2021). New upload to match published version

References in corpus (3)

• Polymer Quantum Mechanics and its Continuum Limit
• An Overview on the Nature of the Bounce in LQC and PQM
• Behavior of the Universe anisotropy in a big-bounce cosmology

Cited by in corpus (24)

• Extended GUP formulation and the role of momentum cut-off
• Exploring the Hubble tension with a late time Modified Gravity scenario
• Dark Energy within the Generalized Uncertainty Principle in Light of DESI DR2
• Emergent Universe Model from Modified Heisenberg Algebra
• Investigation of generalised uncertainty principle effects on FRW cosmology
• Black hole interior quantization: a minimal uncertainty approach
• Modified entropies as the origin of generalized uncertainty principles
• Non-Singular Gravitational Collapse through Modified Heisenberg Algebra
• On the Chandrasekhar Limit in Generalized Uncertainty Principles
• n-dimensional non-commutative GUP quantization and application to the Bianchi I model
• Improved constraints on minimum length models with a macroscopic low loss phonon cavity
• Space and time transformations with a minimal length
• Generalized Uncertainty Principle theories and their classical interpretation
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Fate of Mixmaster Chaos in a Deformed Algebra framework
• Tunnelling-induced cosmic bounce in the presence of anisotropies
• Scalar field inflation driven by a modification of the Heisenberg algebra
• A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Bose-Einstein Condensate and Liquid Helium He${}^4$: Implications of GUP and Modified Gravity Correspondence
• Bouncing Bianchi Models with Deformed Commutation Relations
• Unitary equivalence in Generalized Uncertainty Principle theories
• Mixmaster chaos in a quantum scenario:a Deformed Algebra approach
• An algebraic approach to gravitational quantum mechanics