Spectral distortions to the cosmic microwave background from the recombination of hydrogen and helium
Bibliographic record
Abstract
The recombination of hydrogen and helium at z∼ 1000–7000 gives unavoidable distortions to the cosmic microwave background (CMB) spectrum. We present a detailed calculation of the line intensities arising from the Lyman α (Lyα) (2p–1s) and two-photon (2s–1s) transitions for the recombination of hydrogen, as well as the corresponding lines from helium. We give an approximate formula for the strength of the main recombination line distortion on the CMB in different cosmologies; this peak occurring at about 170 μm. We also find a previously undescribed long-wavelength peak (which we call the pre-recombination peak) from the lines of the 2p–1s transitions, which are formed before significant recombination of the corresponding atoms occurred. Detailed calculations of the two-photon emission-line shapes are presented here for the first time. The frequencies of the photons emitted from the two-photon transition have a wide spectrum and this causes the location of the peak of the two-photon line of hydrogen to be located almost at the same wavelength as the main Lyα peak. The helium lines also give distortions at similar wavelengths, so that the combined distortion has a complex shape. The detection of this distortion would provide direct supporting evidence that the Universe was indeed once a plasma. Moreover, the distortions are a sensitive probe of physics during the time of recombination. Although the spectral distortion is overwhelmed by dust emission from the Galaxy, and is maximum at wavelengths roughly where the cosmic far-infrared background peaks, it may be able to tailor an experiment to detect its non-trivial shape.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".