Investigating the Hubble Constant Tension: Two Numbers in the Standard Cosmological Model
Bibliographic record
Abstract
Abstract The current Hubble constant tension is usually presented by comparing constraints on H 0 only. However, the postrecombination background cosmic evolution is determined by two parameters in the standard ΛCDM model, the Hubble constant (H 0) and today’s matter energy fraction (Ωm). If we therefore compare all constraints individually in the H 0–Ωm plane, (1) various constraints can be treated as independently as possible, (2) single-sided constraints are easier to consider, (3) compatibility among different constraints can be viewed in a more robust way, (4) the model dependence of each constraint is clear, and (5) whether or not a nonstandard model is able to reconcile all constraints in tension can be seen more effectively. We perform a systematic comparison of different constraints in the H 0–Ωm space based on a flat ΛCDM model, treating them as separately as possible. Constraints along different degeneracy directions consistently overlap in one region of the space, with the local measurement from Cepheid variable–calibrated supernovae being the most outlying, followed by the time-delay strong-lensing result. Considering the possibility that some nonstandard physics may reconcile the constraints, we provide a general discussion of nonstandard models with modifications at high, mid, or low redshifts and the effect of local environmental factors. Due to the different responses of individual constraints to a modified model, it is not easy for nonstandard models to reconcile all constraints if none of them have unaccounted-for systematic effects.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".