Bibliographic record
Abstract
We do not observe quantum effects on cosmological scales. Thus, if loop quantum cosmology (LQC) is to provide an accurate depiction of the real world, it must allow for quantum states of spacetime geometry which are semiclassical in two respects: they must be sharply peaked around a single, classical geometry, and they must have small quantum fluctuations. It is generally assumed that Gaussian states exhibit both of these properties. After all, they do in ordinary quantum mechanics. In this paper, we derive exact closed-form expressions for the fluctuations of Gaussian states in LQC and their lower bound given by the Robertson-Schr\"odinger inequality. We demonstrate that, contrary to ordinary quantum mechanics, fluctuations for Gaussian states in spatially flat, homogeneous, and isotropic LQC diverge as the state variance increases (as well as in related cosmological models with the same kinematic Hilbert space and canonical observables). However, when the holonomy length is made to scale with a volume regularization parameter, these fluctuations may be arbitrarily suppressed by taking the fiducial volume to be large, providing analytic control over their divergence. Finally, we show that, despite this, Gaussian states in LQC generally do not minimize uncertainty. Moreover, it is conjectured that no such minimal-uncertainty states exist. Throughout this work, it becomes clear how important the often-assumed condition of holonomy length volume scaling is; we show that when this condition is violated, the resulting theory exhibits operator closure pathologies and other exotic algebraic features.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".