Sample variance for supernovae distance measurements and the Hubble tension
Bibliographic record
Abstract
Recent local measurements of the Hubble constant made using supernovae have delivered a value that differs by $\ensuremath{\sim}5\ensuremath{\sigma}$ (statistical error) from predictions using the cosmic microwave background (CMB), or using baryon acoustic oscillations (BAO) and big-bang nucleosynthesis (BBN) constraints, which are themselves consistent. The effective volume covered by the supernovae is small compared to the other probes, and it is therefore interesting to consider whether sample variance (often also called cosmic variance) is a significant contributor to the offset. We consider four ways of calculating the sample variance: (i) perturbation theory applied to the luminosity distance, which is the most common method considered in the literature; (ii) perturbation of cosmological parameters, as is commonly used to alleviate supersample covariance in sets of N-body simulations; (iii) a new method based on the variance between perturbed spherical top-hat regions; (iv) using numerical N-body simulations. All give consistent results showing that, for the Pantheon supernova sample, sample variance can only lead to fluctuations in ${H}_{0}$ of order $\ifmmode\pm\else\textpm\fi{}1\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ or less. While this is not in itself a new result, the agreement between the methods used adds to its robustness. Furthermore, it is instructive to see how the different methods fit together. We also investigate the internal variance of the ${H}_{0}$ measurement using SH0ES and Pantheon data. By searching for an offset between measurements in opposite hemispheres, we find that the direction coincident with the CMB dipole has a higher ${H}_{0}$ measurement than the opposite hemisphere by roughly $4\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. We compare this with a large number of simulations and find that the size of this asymmetry is statistically likely, but the preference of direction may indicate that further calibration is needed.
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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 | 0.007 | 0.047 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".