A Critical Assessment of CMB Limits on Dark Matter-Baryon Scattering: New Treatment of the Relative Bulk Velocity

TL;DR

This paper introduces a new method to incorporate relative bulk velocities in CMB analysis to set improved limits on dark matter-proton scattering cross sections for specific velocity dependencies, especially for low-mass dark matter.

Contribution

The authors develop a robust iterative approach to include bulk velocity effects in cosmological calculations, refining constraints on dark matter-baryon interactions from CMB data.

Findings

Excluded cross sections: $\sigma_0 > 2.3 imes 10^{-33}~cm^2$ for n=-2

Excluded cross sections: $\sigma_0 > 1.7 imes 10^{-41}~cm^2$ for n=-4

Limits vanish if less than 0.4% of dark matter interacts

Abstract

We perform an improved cosmic microwave background (CMB) analysis to search for dark matter-proton scattering with a momentum-transfer cross section of the form $\sigma_0 v^n$ for $n=-2$ and $n=-4$. In particular, we present a new and robust prescription for incorporating the relative bulk velocity between the dark matter and baryon fluids into the standard linear Boltzmann calculation. Using an iterative procedure, we self-consistently include the effects of the bulk velocities in a cosmology in which dark matter interacts with baryons. With this prescription, we derive CMB bounds on the cross section, excluding $\sigma_0 > 2.3 \times 10^{-33}~\mathrm{cm}^2$ for $n=-2$ and $\sigma_0 > 1.7 \times 10^{-41}~\mathrm{cm}^2$ for $n=-4$ at $95\%$ confidence, for dark matter masses below 10 MeV. Furthermore, we investigate how these constraints change when only a subcomponent of dark matter is interacting. We show that Planck limits vanish if $\lesssim 0.4\%$ of dark matter is tightly coupled to baryons. We discuss the implications of our results for present and future cosmological observations.