The <i>H</i><sub>0</sub> and σ<sub>8</sub> tensions and the scale invariant spectrum
Bibliographic record
Abstract
In a previous communication [1] it was shown that a joint analysis of Cosmic Microwave Background (CMB) data and the current measurement of the local expansion rate favours a model with a scale invariant spectrum (HZP) over the minimal ΛCDM scenario provided that the effective number of relativistic degrees of freedom, N eff , is taken as a free parameter. Such a result is basically obtained due to the Hubble Space Telescope (HST) value of the Hubble constant, H 0 = 73.24 ± 1.74 km . s −1 . Mpc −1 (68% C.L.), as the CMB data alone discard the HZP+ N eff model. Although such a model is not physically motivated by current scenarios of the early universe, observations pointing to a scale invariant spectrum may indicate that the origin of cosmic perturbations lies in an unknown physical process. Here, we extend the previous results performing a Bayesian analysis using joint CMB, HST, and Baryon Acoustic Oscillations (BAO) measurements. In order to take into account the well-known tension on the value of the fluctuation amplitude parameter, σ 8 , we also consider Cluster Number counts (CN) and Weak Lensing (WL) data. We use two different samples of BAO data, which are obtained using two-point spatial (BAO 2PCF) and angular (BAO 2PACF) correlation functions. Our results show that the joint CMB+HST+WL+NC dataset favor the extensions of the ΛCDM model over its minimal parameterization. Also, analysis with the BAO 2PCF always discard the HZP+ N eff model with respect to standard scenario, whereas the combinations using BAO 2PACF favor the former model. We, therefore, find that all dataset disfavor the ΛCDM model with respect to the HZP+ N eff extension, the only exception being the joint analysis with BAO (2PCF).
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".