What can cosmology tell us about gravity? Constraining Horndeski gravity with Sigma and mu
Bibliographic record
Abstract
Phenomenological functions Σ and μ (also known as G light =G and G matter =G) are commonly used to parametrize possible modifications of the Poisson equation relating the matter density contrast to the lensing and the Newtonian potentials, respectively.They will be well constrained by future surveys of large-scale structure.But what would the implications of measuring particular values of these functions be for modified gravity theories?We ask this question in the context of the general Horndeski class of singlefield scalar-tensor theories with second-order equations of motion.We find several consistency conditions that make it possible to rule out broad classes of theories based on measurements of Σ and μ that are independent of their parametric forms.For instance, a measurement of Σ ≠ 1 would rule out all models with a canonical form of kinetic energy, while finding Σ -1 and μ -1 to be of opposite sign would strongly disfavor the entire class of Horndeski models.We separately examine the large-and the smallscale limits, the possibility of scale dependence, and the consistency with bounds on the speed of gravitational waves.We identify subclasses of Horndeski theories that can be ruled out based on the measured difference between Σ and μ.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".