Bibliographic record
Abstract
In this paper we give a coordinate-independent analysis of the dynamics of the spherically symmetric Lemaître–Tolman (LT) cosmologies, emphasizing their relation with the Friedmann–Lemaître (FL) cosmologies. We show that in general, ever-expanding LT cosmologies isotropize at late times, becoming asymptotic to the de Sitter universe or to the Milne universe, depending on whether or not a cosmological constant is present. The rate of isotropization depends significantly on whether Λ > 0 or Λ = 0. We introduce a dimensionless scalar representing the ratio of the Weyl curvature to the Ricci curvature, and show that in both cases it has a finite limit at late times, whose value determines the asymptotic spatial inhomogeneity in various physical quantities. We coin the phrase ‘residual inhomogeneity’ to describe these effects. We also identify the LT cosmologies for which the initial singularity is isotropic, and show that there is a subclass of models that are close-to-FL globally in time and in space.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".