Quantifying the redshift space distortion of the bispectrum III : detection prospects of the multipole moments
Bibliographic record
Abstract
ABSTRACT The redshift space anisotropy of the bispectrum is generally quantified using multipole moments. The possibility of measuring these multipoles in any survey depends on the level of statistical fluctuations. We compute the statistical fluctuations in the measurement of bispectrum multipoles for a Euclid like galaxy survey based on second-order perturbation theory and present two quantities: the signal-to-noise ratio (SNR) which quantifies the detectability of a multipole and the rank correlation which quantifies the correlation in measurement errors between any two multipoles. Based on SNR values, we find that Euclid can potentially measure the bispectrum multipoles up to ℓ = 4 across various triangle shapes, formed by the three k vectors in Fourier space. In general, SNR is maximum for the linear triangles. SNR values also depend on the scales and redshifts of observation. While, ℓ ≤ 2 multipoles can be measured with SNR > 5 even at linear/quasi-linear ($k_1 \lesssim 0.1 \, {\rm Mpc}^{-1}$) scales, for ℓ > 2 multipoles, we require to go to small scales or need to increase bin sizes. These estimates are based on bins of extent Δln k1 = 0.1, Δμ = 0.05, and Δt = 0.05, where k1 is the length of the largest side, and (μ, t), respectively, quantify the size and shape of the triangles. For most multipole pairs, the errors are only weakly correlated across much of the triangle shapes barring a few in the vicinity of squeezed and stretched triangles. This makes it possible to combine the measurements of different multipoles to increase the effective SNR.
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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".