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

Understand

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.