Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance
Bibliographic record
Abstract
Local structure can have important effects on luminosity distance observations, which could for example affect the local estimation of the Hubble constant based on low red-shift type Ia supernovae. Using a spherically symmetric exact solution of the Eistein's equations and a more accurate expansion of the solution of the geodesic equations, we improve the low red-shift expansion of the monopole of the luminosity distance in terms of the curvature function. Based on this we derive the coordinate independent low red-shift expansion of the monopole of the luminosity distance in terms of the monopole of the density contrast. The advantage of this approach is that it relates the luminosity distance directly to density observations, without any dependency on the radial coordinate choice. We compare our formulae to numerical calculations, and find that the formula in terms of the density contrast is in good agreement with the numerical calculations, in the non linear regime is more accurate than the results obtained using linear perturbation theory, especially in the regime of large Laplacian of the perturbations, and is also more accurate than the formula in terms of the curvature function.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".