Investigating cosmic homogeneity using multifractal analysis of the SDSS-IV eBOSS DR16 quasar catalogue
Bibliographic record
Abstract
ABSTRACT We analyse the volume-limited subsamples extracted from the sixteenth data release of the Sloan Digital Sky Survey-IV (SDSS-IV) eBOSS quasar survey spanning a redshift interval of 0.8 < z < 2.2, to estimate the scale of transition to homogeneity in the Universe. The multifractal analysis used for this purpose considers the scaling behaviour of different moments of quasar distribution in different density environments. This analysis gives the spectrum of generalized dimension Dq, where positive values of q characterize the scaling behaviour in overdense regions and the negative ones in underdense regions. We expect fractal correlation dimension Dq(r) = 3, for a homogeneous, random point distribution in 3-Dimensions. The fractal correlation dimension Dq(r), corresponding to q = 2 obtained in our study stabilizes in the range (2.8–2.9) for scales r > 80 h−1 Mpc. The observed quasar distribution shows consistency with the simulated mock data and the random distribution of quasars within one sigma. Further, the generalized dimension spectrum Dq(r) also reveals transition to homogeneity beyond >110 h−1 Mpc, and the dominance of clustering at small scales r < 80 h−1 Mpc. Consequently, our study provides strong evidence for the homogeneity in SDSS quasar distribution, offering insights into large-scale structure properties and, thus can play a pivotal role in scrutinizing the clustering properties of quasars and its evolution in various upcoming surveys such as Dark Energy Spectroscopic Instrument and Extremely Large Telescope.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.006 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".