Perturbative Correction to the Average Expansion Rate of Spacetimes with Perfect Fluids
Bibliographic record
Abstract
This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in the perturbations, and is kept as general as possible. In particular, no approximation such as a long-wavelength or a short-wavelength limit is invoked, and all three types of perturbations (scalar, vector, and tensor) are considered. First, the average value of the expansion rate is computed over a three-dimensional space-like surface where the total density of the fluids is constant. Then, a formula is derived relating that average value to the one over any other surface, on which a different scalar property of the fluids is constant. Moreover, the general formulas giving the correction to the average expansion rate are applied, in particular, to the case of a spacetime containing a single fluid with a constant equation of state. The sign and the effective equation of state of the corresponding back-reaction effect in the first Friedmann equation are examined.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".