Phenomenology of large scale structure in scalar-tensor theories: Joint prior covariance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>w</mml:mi><mml:mi>DE</mml:mi></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math> in Horndeski theories
Bibliographic record
Abstract
Ongoing and upcoming cosmological surveys will significantly improve our ability to probe the equation of state of dark energy, ${w}_{\mathrm{DE}}$, and the phenomenology of large scale structure. They will allow us to constrain deviations from the $\mathrm{\ensuremath{\Lambda}}$ cold dark matter predictions for the relations between the matter density contrast and the weak lensing and the Newtonian potential, described by the functions $\mathrm{\ensuremath{\Sigma}}$ and $\ensuremath{\mu}$, respectively. In this work, we derive the theoretical prior for the joint covariance of ${w}_{\mathrm{DE}}$, $\mathrm{\ensuremath{\Sigma}}$ and $\ensuremath{\mu}$, expected in general scalar-tensor theories with second order equations of motion (Horndeski gravity), focusing on their time-dependence at certain representative scales. We employ Monte Carlo methods to generate large ensembles of statistically independent Horndeski models, focusing on those that are physically viable and in broad agreement with local tests of gravity, the observed cosmic expansion history and the measurement of the speed of gravitational waves from a binary neutron star merger. We identify several interesting features and trends in the distribution functions of ${w}_{\mathrm{DE}}$, $\mathrm{\ensuremath{\Sigma}}$ and $\ensuremath{\mu}$, as well as in their covariances; we confirm the high degree of correlation between $\mathrm{\ensuremath{\Sigma}}$ and $\ensuremath{\mu}$ in scalar-tensor theories. The derived prior covariance matrices will allow us to reconstruct jointly ${w}_{\mathrm{DE}}$, $\mathrm{\ensuremath{\Sigma}}$ and $\ensuremath{\mu}$ in a nonparametric way.
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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 | 0.005 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".