Exact treatment of weak dark matter-baryon scattering for linear-cosmology observables
Bibliographic record
Abstract
Elastic scattering of dark matter (DM) particles with baryons induce cosmological signals that may be detectable with modern or future telescopes. For DM-baryon scattering cross sections scaling with negative powers of relative velocity, ${\ensuremath{\sigma}}_{\ensuremath{\chi}b}(v)\ensuremath{\propto}{v}^{\ensuremath{-}2},{v}^{\ensuremath{-}4}$, such interactions introduce a momentum-exchange rate that is nonlinear in DM-baryon bulk relative velocities, thus not amenable for inclusion as-is into standard linear cosmological Boltzmann codes. Linear Ans\"atze have been adopted in past works, but their accuracy is unknown as they do not arise from first-principles derivations. In this work, for the first time, we construct a rigorous framework for computing linear-cosmology observables as a perturbative expansion in ${\ensuremath{\sigma}}_{\ensuremath{\chi}b}$. We argue that this approach is accurate for cosmic microwave background (CMB) angular power spectra when most or all of the DM is scattering with baryons with cross section ${\ensuremath{\sigma}}_{\ensuremath{\chi}b}(v)\ensuremath{\propto}{v}^{\ensuremath{-}2},{v}^{\ensuremath{-}4}$. We derive exact formal expressions for CMB power spectra at linear order in ${\ensuremath{\sigma}}_{\ensuremath{\chi}b}$, and show that they only depend on a specific velocity integral of the momentum-exchange rate. Consequently, we can obtain the exact power spectra at linear order in ${\ensuremath{\sigma}}_{\ensuremath{\chi}b}$ by substituting the original nonlinear momentum-exchange rate with a uniquely specified linear rate. Serendipitously, we find that the exact substitution we derive from first principles precisely coincides with the most widely used linear Ansatz, thus placing previous CMB-anisotropy upper bounds on more solid footing. In addition to finally providing an exact cosmological solution to the DM-baryon scattering problem in a well-defined region of parameter space, the framework we construct opens the way to computing higher-order correlation functions, beyond power spectra, which are promising, yet unexplored, probes of DM-baryon scattering.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".