Dark Matter–Baryon Scattering

• Dark matter–baryon scattering is defined as non-gravitational interactions between dark matter and baryonic particles that exchange momentum and energy via contact, mediator, or exotic processes.
• Theoretical models use Galilean-invariant operators and velocity-dependent cross sections to predict its impact on the cosmic microwave background, matter power spectrum, and 21 cm cosmology.
• Observational probes from CMB anisotropies, Lyman-α forests, and 21 cm experiments provide actionable constraints on dark matter properties and the evolution of cosmic structure.

Dark matter–baryon (DM–b) scattering refers to any non-gravitational interaction between dark matter and baryonic (i.e., Standard Model) particles—principally nucleons and electrons—that leads to a measurable exchange of momentum and/or energy in astrophysical or cosmological environments. Such interactions can occur via direct contact terms, exchange of light mediators, or through more exotic mechanisms involving continuum states. DM–baryon scattering impacts the thermal, kinetic, and structural evolution of the cosmic plasma, leaving signatures in the cosmic microwave background (CMB), matter power spectrum, 21 cm line, structure formation, and terrestrial experiments.

1. Theoretical Frameworks for Dark Matter–Baryon Scattering

The nonrelativistic effective theory underlying direct and indirect DM–baryon scattering is constructed from Galilean-invariant operators built from the DM–baryon momentum transfer $\mathbf{q}$, the perpendicular velocity $\mathbf{v}_\perp$, and the DM/nucleon spin vectors $\mathbf{S}_\chi$ and $\mathbf{S}_N$ (Katz et al., 2015). Up to momentum-suppressed terms, a complete set consists of 15 operators $O_1 ... O_{15}$, such as:

• $O_1 = 1$ (spin-independent, contact)
• $O_4 = \mathbf{S}_\chi \cdot \mathbf{S}_N$ (spin-dependent), etc.

Each microphysical model maps onto specific combinations of these operators. The amplitude $\mathcal{M}_0$ for DM–baryon scattering can be modified by mediator dynamics.

Velocity-Dependent Cross Sections:

Common parametrizations include a power-law scaling $\sigma(v) = \sigma_0 v^n$, where $n$ is process-dependent:

• $n = 0$: s-wave, contact-like (heavy mediator)
• $n = -2, -4$: electric/magnetic dipole or Coulomb/Rutherford-like (arising from light or continuum mediators)

Such velocity dependencies control the redshift of maximal impact: for $n > -3$, effects dominate at high velocities (early times, CMB), while for $n < -3$, low-velocity (later, during 21 cm epoch and structure formation) constraints become powerful (Dvorkin et al., 2013).

Continuum Mediators:

Instead of a single particle or contact, the exchange of a continuum of mediator states (e.g., near-conformal sectors) modifies the matrix element by a universal form factor $f(q^2) \propto (q^2/\Lambda^2)^{d-2}$, where $d$ is the mediator scaling dimension and $\Lambda$ the suppression scale. This leads to differential recoil spectra interpolating between contact and massless mediator cases, and is constrained by cosmology, direct detection, beam-dump, and collider probes (Katz et al., 2015).

2. Cosmological and Astrophysical Consequences

Cosmic Microwave Background (CMB):

DM–b scattering imprints on the CMB primarily through momentum-drag and thermal exchange, entering linearly into the Boltzmann hierarchy as an additional drag term: $$\dot\theta_\chi = \cdots + R_\chi(\theta_b - \theta_\chi)$$ where $R_\chi \propto \langle v_\text{rel}^{3+n} \rangle$ for $\sigma \propto v^n$. High-precision Planck CMB anisotropy and polarization data currently set the tightest bounds, e.g., for $n = -4$ and $m_\chi \lesssim 1\,\mathrm{GeV}$, $$\sigma_0 \lesssim 1.7 \times 10^{-41}\,\mathrm{cm}^2$$ (Boddy et al., 2018, Dvorkin et al., 2013, Xu et al., 2018). The effect of velocity-dependent drag, including the nonlinearity in the DM–baryon relative velocity distribution, has been systematically incorporated via iterative methods and, more recently, via a perturbative expansion in the cross-section (Ali-Haïmoud et al., 2023). The latter formalism rigorously justifies widely used "mean-field" (velocity-averaged) replacements in Boltzmann codes as exact at linear order, closing previous theoretical loopholes.

Large-Scale Structure (LSS):

Elastic scattering damps small-scale power in the matter power spectrum by collisional (drag-induced) suppression, producing a step-like deficit at $k \gtrsim k_\text{damp}$. Combined fits to Planck, BOSS, and weak lensing (DES-Y3) yield $95\%$ C.L. upper limits for velocity-independent scattering (n=0) around $\sigma_0 \sim 2 \times 10^{-26}\,\mathrm{cm}^2$ for $m_\chi = 1\,\mathrm{MeV}$ if all DM interacts, with hints ($\gtrsim 2\sigma$) of nonzero interactions when only a subcomponent ($f_\chi \sim 10\%$) is involved (He et al., 4 Feb 2025, He et al., 2023). Such suppression partly relieves the $S_8$ tension between Planck and LSS surveys.

Thermal and Ionization History:

DM–baryon heat exchange modifies the thermal evolution of the baryons and dark sector, producing colder baryons after CMB decoupling and affecting the evolution of the intergalactic medium (IGM). The net heating/cooling rate per baryon generally takes the form: $$\frac{dQ_b}{dt} = \Gamma_{b\chi}(T_\chi - T_b) + (\cdots)\, D(V_\text{rel}) V_\text{rel}^2$$ where $\Gamma_{b\chi}$ is the thermal exchange rate term and $D(V_\text{rel})$ encodes the drag (frictional heating) arising from bulk flows (Muñoz et al., 2015, Tashiro et al., 2014). Observationally, Lyman-$\alpha$ forest measurements of $T_\text{IGM}$ at $z \sim 5$ imply $$\sigma_\text{phys} \lesssim 10^{-20}\,\mathrm{cm}^2$$ for $m_\chi \lesssim 1\,\mathrm{GeV}$, independent of the velocity scaling for $n \leq 0$ (Muñoz et al., 2017).

21 cm Cosmology:

Scattering models with $\sigma \propto v^{-4}$ and $m_\chi \lesssim$ GeV can efficiently cool IGM baryons during the cosmic dark ages ($30 \lesssim z \lesssim 200$), deepening the 21 cm absorption trough (as reported by EDGES) and enhancing fluctuations. The global and fluctuating 21 cm signals depend sensitively on the nature of DM–baryon coupling, allowing constraints or potential discovery via current (EDGES), forthcoming (SKA, HERA), and lunar (Hongmeng/DSL) experiments (Muñoz et al., 2015, Cang et al., 4 Dec 2025, Fialkov et al., 2018). Specifically, Hongmeng is forecasted to reach $\sigma_0 \lesssim 4 \times 10^{-43}\,\mathrm{cm}^2$ over $0.1\,\mathrm{MeV} < m_\chi < 0.4\,\mathrm{GeV}$ after five years (Cang et al., 4 Dec 2025).

3. Methodological Developments: Fluid, Fokker-Planck, and Phase-Space Approaches

Linear Theory and Boltzmann Codes:

Standard cosmological codes (e.g., CLASS, CAMB) implement DM–baryon interactions by treating DM as a thermal Maxwell–Boltzmann (MB) fluid and adding drag/heating terms to the velocity and temperature evolution equations. The fluid approach is justified in the strong self-interaction regime but misestimates the rates when DM self-scattering is weak (Ali-Haïmoud, 2018, Gandhi et al., 2022).

Boltzmann–Fokker-Planck (BFP) Formalism:

To address deficiencies of the MB ansatz, Ali-Haïmoud introduced a Boltzmann–Fokker-Planck (BFP) hierarchy: the full phase-space collisional Boltzmann equation is replaced by a Fokker-Planck equation that preserves exact momentum and heat exchange rates and recovers MB as a special (detailed-balance) case. Numerical solutions show that the FP approximation maintains errors $< 17\%$ versus the exact phase-space equation (much better than MB's $>100\%$ discrepancies for steep $n$) (Ali-Haïmoud, 2018, Gandhi et al., 2022). The FP formalism supports analyses even in the weak self-interaction regime and for non-thermal DM velocity distributions.

Perturbative and Nonlinear Velocity Treatments:

Treatment of the nonlinear dependence on the DM–baryon bulk relative velocity is crucial for $n < 0$. Recent work rigorously derives, to leading order in the cross-section, the unique mean-field drag rate via a perturbative expansion, confirming the validity of previous "mean-field" MB-based substitutions (Ali-Haïmoud et al., 2023). For significant interacting subcomponents ($f_\chi < 0.4\%$), limits rapidly vanish as the effective coupling is diluted and the interacting component tracks baryon velocities (Boddy et al., 2018).

4. Experimental and Observational Constraints

Probe	Sensitivity $n$	Key Limit(s) (for $m_\chi \lesssim$ GeV)	Reference
CMB (Planck)	-4, -2, 0	$\sigma_0 \lesssim 1.7 \times 10^{-41}$ cm$^2$ ($n=-4$)	(Boddy et al., 2018, Xu et al., 2018)
Lyman-$\alpha$	-4 to 0	$\sigma_\text{phys} \lesssim 10^{-20}$ cm$^2$	(Muñoz et al., 2017)
21 cm (Hongmeng)	-4	$\sigma_0 \lesssim 4 \times 10^{-43}$ cm$^2$	(Cang et al., 4 Dec 2025)
JWST UVLF	-4, -2, 0	$\log_{10}[\sigma_{-2}/\mathrm{cm}^2] < -33.5$ (for $m_\chi=100$ MeV)	(Das et al., 4 Nov 2025)
Direct detection	0	$\sigma_p^\text{SI} \lesssim 10^{-45}$ cm$^2$ ($m_\chi \sim 100$ GeV)	(Katz et al., 2015)
Terrestrial (Earth)	$v$-dependent	$\sigma_{1\,\mathrm{km/s}} \lesssim 10^{-28}$ cm$^2$ ($\lesssim$GeV)	(Neufeld et al., 2018)

Limits are process, scale, and mass dependent; details must account for velocity dependence and experiment redshift sensitivity. CMB (anisotropies & spectral distortions), Lyman-$\alpha$ forest, and 21 cm observations provide complementary constraints across mass and $n$ ranges; direct detection dominates for heavy DM, while terrestrial and orbit-based limits become relevant for strongly interacting light DM.

5. Key Phenomenological Impacts and Discovery Prospects

• Structure formation: DM–baryon interactions can erase small-scale power, potentially delaying or suppressing formation of the first stars and galaxies. JWST rest-UV luminosity functions at $z>10$ now provide robust limits, especially for $n=-2$ models (Das et al., 4 Nov 2025).
• Cosmic dawn/cooling: Baryonic gas can be cooled below the standard adiabatic floor via $v^{-4}$-dependent scattering, yielding the large 21 cm absorption observed by EDGES. Allowed parameter space is strongly constrained by timing (star formation onset) and concordance with Pop III–host abundances (Liu et al., 2019, Fialkov et al., 2018).
• Power spectrum signatures: The step-like suppression of $P(k)$ at $k > k_{\text{damp}}$ (LSS, $S_8$ tension domain) and the scale-independent suppression of the 21 cm angular power spectrum, as well as the order-of-magnitude boost of temperature/brightness perturbations, are robust predictions (He et al., 2023, Short et al., 2022, Tashiro et al., 2014).
• Baryon acoustic oscillations (BAO): Velocity-dependent DM–b scattering excites large-amplitude BAO features in the cosmic dawn 21 cm power spectrum, potentially offering unambiguous evidence of DM–baryon interactions (Fialkov et al., 2018).
• Laboratory anomalies: Strongly interacting DM with $m_\chi \sim 1$ GeV and large $\sigma_0$ is excluded by the lifetime of LHC proton beams, low-Earth-orbit spacecraft orbital decay, cryogen vaporization, and crustal conductivity constraints (Neufeld et al., 2018).

6. Future Directions and Open Problems

Major outstanding avenues include:

• Improved Boltzmann solvers: Implementation of the Fokker-Planck formalism in public cosmological codes (e.g., CLASS, CAMB) is underway, promising systematic accuracy improvements for upcoming CMB-S4 and LSS surveys (Ali-Haïmoud, 2018, Gandhi et al., 2022).
• Synergy of high-$z$ probes: Simultaneous analysis of CMB, Lyman-$\alpha$, JWST, 21 cm, and Milky Way satellite data will refine or close currently viable DM–baryon scattering windows.
• Nonlinear and small-fraction scenarios: Non-perturbative treatments are needed for scenarios with small scattering subcomponents ($f_\chi \ll 1$) or very strong coupling.
• Exotic mediators and continuum effects: Spectral distortions, binned recoil spectra, and collider/beam-dump searches provide additional handles on continuum-mediated and dark sector scenarios (Katz et al., 2015).
• Stochastic heating/cooling and reionization: Detailed modeling of inhomogeneities during cosmic dawn and reionization, including the impact of velocity fields and anisotropic scattering, is essential for robust interpretation of future 21 cm global and tomographic measurements (Short et al., 2022, Cang et al., 4 Dec 2025).

Current and next-generation astrophysical surveys, together with advancing theoretical frameworks for DM–baryon scattering, provide an increasingly stringent—and multi-faceted—probe of the particle physics of dark matter over orders of magnitude in mass, cross-section, and interaction structure.