Polymer quantum cosmology: Lifting quantization ambiguities using a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>SL</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:mrow></mml:math> conformal symmetry
Bibliographic record
Abstract
In this paper, we stress that the simplest cosmological model consisting in a massless scalar field minimally coupled to homogeneous and isotropic gravity has an built-in $\mathrm{SL}(2,\mathbb{R})$ symmetry. Protecting this symmetry naturally provides an efficient way to constrain the quantization of this cosmological system whatever the quantization scheme and allows one, in particular, to fix the quantization ambiguities arising in the canonical quantization program. Applying this method to the loop quantization of the Friedmann-Lemaitre-Robertson-Walker cosmology leads to a new loop quantum cosmology model that preserves the $\mathrm{SL}(2,\mathbb{R})$ symmetry of the classical system. This new polymer regularization consistent with the conformal symmetry can be derived as a nonlinear canonical transformation of the classical Friedmann-Lemaitre-Robertson-Walker 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. Three-dimensional scale transformations, generated by the dilatation operator, are realized as unitary transformations despite the minimal length scale hard coded 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 semiclassical regime at large volume. The technical details of the construction of this model are presented in a longer companion paper [J. B. Achour and E. R. Livine, arXiv:1904.06149].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".