Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry

Abstract

In this letter, we stress that the simplest cosmological model consisting in a massless scalar field minimally coupled to homogeneous and isotropic gravity has an in-built $\SL(2,\mathbb{R})$ symmetry. Protecting this symmetry naturally provides an efficient way to constrain the quantization of this cosmological system whatever the quantization scheme and allows in particular to fix the quantization ambiguities arising in the canonical quantization program. Applying this method to the loop quantization of the FLRW cosmology leads to a new loop quantum cosmology model which preserves the $\SL(2,\mathbb{R})$ symmetry of the classical system. This new polymer regularization consistent with the conformal symmetry can be derived as a non-linear canonical transformation of the classical FLRW phase space, which maps the classical singular dynamics into a regular effective bouncing dynamics. This improved regularization preserves the scaling properties of the volume and Hamiltonian constraint. 3d scale transformations, generated by the dilatation operator, are realized as unitary transformations despite the minimal length scale hardcoded in the theory. Finally, we point out that the resulting cosmological dynamics exhibits an interesting duality between short and long distances, reminiscent of the T-duality in string theory, with the near-singularity regime dual to the semi-classical regime at large volume. The technical details of the construction of this model are presented in a longer companion paper \cite{BenAchour:2019ywl}.

8 pages, match the published version in PRD

References in corpus (10)

• Polymer Quantum Mechanics and its Continuum Limit
• Quantum cosmology: a review
• Self-dual Black Holes in LQG: Theory and Phenomenology
• Dynamical coherent states and physical solutions of quantum cosmological bounces
• Hamiltonian and physical Hilbert space in polymer quantum mechanics
• Polymer state approximations of Schroedinger wave functions
• Coarse graining as a representation change
• Factor ordering and large-volume dynamics in quantum cosmology
• Inflationary Cosmology, Diffeomorphism Group of the Line and Virasoro Coadjoint Orbits
• Quantum cosmology for the 21st century: A debate

Cited by in corpus (15)

• An Overview on the Nature of the Bounce in LQC and PQM
• Coarse graining as a representation change
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Symmetries of the Black Hole Interior and Singularity Regularization
• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• The Cosmological Spinor
• Non-bouncing solutions in loop quantum cosmology
• Dynamical symmetries of homogeneous minisuperspace models
• Quantization of dynamical symplectic reduction
• Quantization of time and the big bang via scale-invariant loop gravity
• Group quantization of the black hole minisuperspace
• Conformal structure of FLRW Cosmology: Spinorial representation and the so(3,2) algebra of observables
• Tunneling dynamics in cosmological bounce models
• The Cosmological Constant from Conformal Transformations: Möbius Invariance and Schwarzian Action
• Cosmology as a CFT${}_1$