Boltzmann-Fokker-Planck formalism for dark-matter--baryon scattering

Abstract

Linear-cosmology observables, such as the Cosmic Microwave Background (CMB), or the large-scale distribution of matter, have long been used as clean probes of dark matter (DM) interactions with baryons. It is standard to model the DM as an ideal fluid with a thermal Maxwell-Boltzmann (MB) velocity distribution, in order to compute the heat and momentum-exchange rates relevant to these probes. This approximation only applies in the limit where DM self-interactions are frequent enough to efficiently redistribute DM velocities. It does not accurately describe weakly self-interacting particles, whose velocity distribution unavoidably departs from MB once they decouple from baryons. This article lays out a new formalism required to accurately model DM-baryon scattering, even when DM self-interactions are negligible. The ideal fluid equations are replaced by the collisional Boltzmann equation for the DM phase-space distribution. The collision operator is approximated by a Fokker-Planck operator, constructed to recover the exact heat and momentum exchange rates, and allowing for an efficient numerical implementation. Numerical solutions to the background evolution are presented, which show that the MB approximation can over-estimate the heat-exchange rate by factors of ~ 2-3, especially for light DM particles. A Boltzmann-Fokker-Planck hierarchy for perturbations is derived. This new formalism allows to explore a wider range of DM models, and will be especially relevant for upcoming ultra-high-sensitivity CMB probes.

arXiv comment18 pages, 3 figures. Version accepted for publication in PRD after minor additions

References in corpus (46)

• Supersymmetric Dark Matter
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Planck 2013 results. I. Overview of products and scientific results
• An absorption profile centred at 78 megahertz in the sky-averaged spectrum
• The Effective Field Theory of Dark Matter Direct Detection
• Possible interaction between baryons and dark-matter particles revealed by the first stars
• CMB Constraints on WIMP Annihilation: Energy Absorption During the Recombination Epoch
• Particle decays during the cosmic dark ages
• Dark matter direct-detection experiments
• Model-independent WIMP Scattering Responses and Event Rates: A Mathematica Package for Experimental Analysis
• Constraining Dark Matter-Baryon Scattering with Linear Cosmology
• A review of indirect searches for particle dark matter
• Dark-Matter Electric and Magnetic Dipole Moments
• Insights on Dark Matter from Hydrogen during Cosmic Dawn
• HyRec: A fast and highly accurate primordial hydrogen and helium recombination code
• Particle Models and the Small-Scale Structure of Dark Matter
• Signs of Dark Matter at 21-cm?
• Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations
• Constraining Dark Matter candidates from structure formation
• Early-Universe Constraints on Dark Matter-Baryon Scattering and their Implications for a Global 21cm Signal
• Dark Matter Searches at Colliders
• Probing sub-GeV Dark Matter-Baryon Scattering with Cosmological Observables
• Constraining Baryon--Dark Matter Scattering with the Cosmic Dawn 21-cm Signal
• A refined model for spinning dust radiation
• Tighter Limits on Dark Matter Explanations of the Anomalous EDGES 21cm Signal
• Constraints on scattering of keV--TeV dark matter with protons in the early Universe
• A Critical Assessment of CMB Limits on Dark Matter-Baryon Scattering: New Treatment of the Relative Bulk Velocity
• Constraining Dark Matter-Neutrino Interactions using the CMB and Large-Scale Structure
• Heating of Baryons due to Scattering with Dark Matter During the Dark Ages
• Narrowing the window for millicharged particles by CMB anisotropy
• Interacting Dark Matter disguised as Warm Dark Matter
• Constraints on dark matter interactions with standard model particles from CMB spectral distortions
• Cosmological bounds on dark matter-neutrino interactions
• The Effects of Dark Matter-Baryon Scattering on Redshifted 21 cm Signals
• Form factors for dark matter capture by the Sun in effective theories
• Cosmic microwave background and large scale structure limits on the interaction between dark matter and baryons
• Using the CMB angular power spectrum to study Dark Matter-photon interactions
• Kinetic decoupling of neutralino dark matter
• 21-cm Fluctuations from Charged Dark Matter
• First Cosmological Constraint on the Effective Theory of Dark Matter-Proton Interactions
• Matter Power Spectrum in Hidden Neutrino Interacting Dark Matter Models: A Closer Look at the Collision Term
• Lyman-alpha transfer in primordial hydrogen recombination
• Disentangling Dark Physics with Cosmic Microwave Background Experiments
• Effects of electrically charged dark matter on cosmic microwave background anisotropies
• Small Second Acoustic Peak from Interacting Cold Dark Matter?

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