Constraining Dark Matter-Baryon Scattering with Linear Cosmology

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.

• The paper derives stringent upper limits on dark matter–baryon scattering cross sections using linear perturbation theory and cosmological data.
• It employs modified Boltzmann equations and CAMB code to assess velocity-dependent interactions that affect early Universe density perturbations.
• Results indicate that significant dark matter–baryon interactions are unlikely in large halos, refining models of structure formation.

Constraints on Dark Matter-Baryon Scattering from Linear Cosmology

The paper "Constraining Dark Matter-Baryon Scattering with Linear Cosmology," authored by Cora Dvorkin, Kfir Blum, and Marc Kamionkowski, explores the constraints on elastic scattering between baryons and dark matter (DM) through cosmic microwave background (CMB) data from the Planck satellite and Lyman-$\alpha$ forest data from the Sloan Digital Sky Survey. The primary focus is to rigorously assess the limitations on DM-baryon interactions using these datasets.

Background and Motivation

Traditional dark matter candidates, like weakly-interacting massive particles (WIMPs), are postulated to interact only gravitationally with regular matter. However, the null results from LHC searches and discrepancies in simulations highlight the necessity of considering stronger DM-baryon interactions. This paper evaluates how these interactions impact the dynamics of linear density perturbations in the early Universe and offers constraints on the cross-section formulas, particularly those depending on the relative velocity of DM and baryons, given as $\sigma \propto v^n$ for a wide range of $n$.

Methodology and Analysis

The method involves deriving the DM-baryon momentum transfer rate from the linear theory of cosmological perturbations. This requires solving modified linear Boltzmann equations, factoring in the interplay between bulk and thermal velocities. The authors use high-redshift data, making a crucial assumption that peculiar velocity is small compared to the thermal velocity at these redshifts. The transition at $z \sim 10^4$ is pivotal, where peculiar velocities become significant relative to thermal velocities, demanding a nonlinear treatment.

Key Constraints and Results

1. Parameter Constraints: By integrating this interaction into the CAMB code, the authors compute the constraints on DM-baryon scattering across different parameter spaces, expressed as $(\sigma_0/m_\chi)$ where $\sigma_0$ is the cross-section at a reference velocity.
2. Velocity Dependence: The parameter $n$ plays a critical role in altering suppression behaviors of small-scale structures. For instance, models with $n = -4$, like those involving DM millicharge, show minimal impact on the halo mass function as they freeze out at high redshifts.
3. Mass Function Impact: It is emphasized that DM-baryon interactions cannot affect the halo mass function for halos with masses larger than $10^{12} M_\odot$, setting an upper threshold consistent with current cosmic observations.
4. Model-Independent Results: The study provides an essential upper limit on the interaction rate, demonstrating that significant baryon-DM interactions are precluded in a galaxy like the Milky Way, throughout its history. This is a robust, model-independent result under the assumption that the DM constituting galactic structures is the same as that affecting early-universe perturbations.

Implications and Future Directions

The work underscores that DM-baryon cross sections are tightly constrained by existing cosmological data, limiting their influence on both early Universe dynamics and nonlinear structures like galaxies. These findings have important implications for models predicting small-scale structure formation and underscore the effectiveness of combined CMB and Lyman-$\alpha$ data in testing DM properties.

Moving forward, addressing the non-Gaussian and nonlinear effects more thoroughly, especially during redshifts less than $10^4$, would refine the current analysis. Further simulations might also explore residual small-scale effects to better understand DM interactions and, potentially, offer insights relevant to alternative dark matter models beyond collisionless assumptions.

In conclusion, this paper delivers a comprehensive analysis of DM-baryon interactions using linear cosmological frameworks, offering vital constraints that inform both theoretical and observational astrophysics regarding the nature and behavior of dark matter.