Constraining Dark Matter-Baryon Scattering with Linear Cosmology

TL;DR

The paper develops a model‑independent framework to constrain elastic baryon–dark-matter scattering with cross sections σ ∝ v^n (−4 ≤ n ≤ 2) by integrating linear cosmology perturbation theory with Planck CMB data and Ly‑α forest measurements. It derives the DM drag force, modifies the Boltzmann equations, and analyzes the interplay between thermal and bulk velocities, including a mean-field extension to handle nonlinearities at z < 10^4. Using MCMC with Planck and Ly‑α data, it places 95% CL bounds on σ0/mχ that are notably strengthened by Ly‑α data for n > −3, and discusses how these constraints translate into the halo mass function, showing no impact on halos above ~10^12 M⊙. The results imply that any baryon–DM scattering would be negligible within Milky Way-like environments over cosmic time, while highlighting potential nonlinear and non-Gaussian effects in certain velocity regimes that warrant future study.

Abstract

We derive constraints on elastic scattering between baryons and dark matter using the cosmic microwave background (CMB) data from the Planck satellite and the Lyman-alpha forest data from the Sloan Digital Sky Survey. Elastic scattering allows baryons and dark matter to exchange momentum, affecting the dynamics of linear density perturbations in the early Universe. We derive constraints to scattering cross sections of the form sigma \propto v^n, allowing for a wide range of velocity dependencies with n between -4 and 2. We improve and correct previous estimates where they exist, including velocity-independent cross section as well as dark matter millicharge and electromagnetic dipole moments. Lyman-alpha forest data dominates the constraints for n>-3, where the improvement over CMB data alone can be several orders of magnitude. Dark matter-baryon scattering cannot affect the halo mass function on mass scales M>10^{12} M_{solar}. Our results imply, model-independently, that a baryon in the halo of a galaxy like our own Milky Way, does not scatter from dark matter particles during the age of the galaxy.

Figures (5)

• Figure 1: Cosmological proton thermal velocity (blue), and peculiar baryon-DM relative velocity (green). The redshifts probed by CMB and Lyman-$\alpha$ forest measurements are roughly marked by blue and orange boxes, respectively.
• Figure 2: Momentum-transfer rate $R_\chi$ vs. redshift for different values of $n$ between -4 to +2. All of the curves are normalized to satisfy a mean free path of $\sim0.5$ Mpc for proton scattering on DM at the MW solar cycle; see Eq. (\ref{['eq:SS']}) and the discussion around it.
• Figure 3: Left panel: Relative difference of the CMB power spectra of models with different velocity-dependent cross sections to the best fit $\Lambda$CDM model. The cross sections of the different models correspond to the 95%CL limit from the CMB $+$ Lyman-$\alpha$ analysis (see Tab. \ref{['tab:1']}), while all other cosmological parameters are taken to optimize the likelihood for this given cross section. Right panel: Matter power spectra at $z=3$. The data point corresponds to the linear theory best fit amplitude using Lyman-$\alpha$ data from McDonald:2004xn. The error bar corresponds to the $95\%$ CL limit on the amplitude. The black band denotes the range of linear matter power spectra slopes allowed at the $95\%$ CL limit at $k=1.03$ h/Mpc.
• Figure 4: Slope $d\ln{P}/d\ln{k}$ for the different models, as a function of wave number. The data point corresponds to the best fit value of the linear matter power spectrum slope from the Lyman-$\alpha$ measurement in Ref. McDonald:2004xn, and the error bar on the point corresponds to the $95\%$ CL limit.
• Figure 5: Halo mass function as a function of mass. A model with no scattering is shown in black/dashed lines, and models with different velocity-dependent cross sections are shown with a value of $\sigma_0/m_\chi$ taken at the $95\%$ CL limit from the analysis with CMB and Lyman-$\alpha$ data in Table \ref{['tab:1']}.