Bibliographic record
Abstract
Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously complicated. Our goal in this paper is to formulate the governing equations for linear perturbation theory in a particularly simple and concise form in order to facilitate the extension to nonlinear perturbations. Our approach has several novel features. We show that the use of so-called intrinsic gauge invariants has two advantages. It naturally leads to: (i) a physically motivated choice of a gauge invariant associated with the matter density, and (ii) two distinct and complementary ways of formulating the evolution equations for scalar perturbations, associated with the work of Bardeen and of Kodama and Sasaki. In the first case the perturbed Einstein tensor gives rise to a second order (in time) linear differential operator, and in the second case to a pair of coupled first order (in time) linear differential operators. These operators are of fundamental importance in cosmological perturbation theory, since they provide the leading order terms in the governing equations for nonlinear perturbations.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".