The effect of forbidden transitions on cosmological hydrogen and helium recombination
Bibliographic record
Abstract
More than half of the atoms in the Universe recombined via forbidden transitions, so that accurate treatment of the forbidden channels is important in order to follow the cosmological recombination process with the level of precision required by future microwave anisotropy experiments. We perform a multilevel calculation of the recombination of hydrogen (H) and helium (He) with the addition of the 23P1–11S0 spin-forbidden transition for neutral helium (He i), plus the nS–1S and nD–1S two-photon transitions for H (up to n= 40) and among singlet states of He i (n≤ 10 and ℓ≤ 7). The potential importance of such transitions was first proposed by Dubrovich & Grachev using an effective three-level atom model. Here, we relax the thermal equilibrium assumption among the higher excited states to investigate the effect of these extra forbidden transitions on the ionization fraction xe and the cosmic microwave background (CMB) angular power spectrum Cℓ. The spin-forbidden transition brings more than 1 per cent change in xe. The two-photon transitions may also give non-negligible effects, but currently accurate rates exist only for n≤ 3. We find that changes in both xe and Cℓ would be at about the per cent level with the approximate rates given by Dubrovich & Grachev. However, the two-photon rates from 3S to 1S and 3D to 1S of H appear to have been overestimated, and our best numerical calculation puts the effect on xe and Cℓ at below the per cent level. Nevertheless, we do not claim that we have the definite answer, since several issues remain open; sub-per cent level computation of the Cℓ values requires improved calculations of atomic transition rates as well as increasingly complex multilevel atom calculations.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".