Constraints on Dark Matter interactions from structure formation: Damping lengths

TL;DR

This work develops a comprehensive, theory-driven framework to constrain Dark Matter interactions through damping of primordial fluctuations. By expressing transport coefficients (shear viscosity, heat conduction, and bulk viscosity) as sums over species in a composite DM fluid, it derives diffuse damping scales, including self-damping, induced-damping, mixed-damping, and free-streaming, up to the epoch of decoupling. The authors classify DM candidates in a two-parameter space defined by DM mass m_dm and reduced interaction rate Γ̃, delineating six regions (I–VI) with region-specific limits, and explicitly analyze DM–neutrino and DM–photon couplings under URFO and NRFO relic-density scenarios. They show that neutrino-induced damping can be particularly constraining, even in mixed-damping regimes, while photon-induced damping imposes strong but more model-dependent bounds, all yielding a generalized DM classification beyond standard CDM, WDM, and HDM paradigms. Overall, the results establish necessary conditions on DM mass and interaction rates that preserve observed structure formation and provide a framework for evaluating DM candidates across a vast parameter space, with detailed astrophysical implications to be explored in a companion paper.

Abstract

(Shortened) Weakly Interacting Massive Particles are often said to be the best Dark Matter candidates. Studies have shown however that rather large Dark Matter-photon or Dark Matter-baryon interactions could be allowed by cosmology. Here we address the question of the role of the Dark Matter interactions in more detail to determine at which extent Dark Matter has to be necessarily weakly interacting. To this purpose, we compute the collisional damping (and free-streaming) lengths of generic interacting Dark Matter candidates and compare them to the scale of the smallest primordial structures known to exist in the Universe. We obtain necessary conditions that any candidate must satisfy. We point out the existence of new Dark Matter scenarios and exhibit new damping regimes. For example, an interacting candidate may bear a similar damping than that of collisionless Warm Dark Matter particles. The main difference is due to the Dark Matter coupling to interacting (or even freely-propagating) species. Our approach yields a general classification of Dark Matter candidates which extends the definitions of the usual Cold, Warm and Hot Dark Matter scenarios when interactions, weak or strong, are considered.

Figures (9)

• Figure 1: Bounds in the [Dark Matter particles' mass, Dark Matter interaction rate] parameter space obtained from self-damping and free-streaming. The interaction rate $\widetilde{\Gamma}_{dec(dm)}$ is $\Gamma_{dec(dm)} a^3$ taken at the Dark Matter decoupling. The labels I to VI correspond to different scenarios. The hatches indicate which part of the parameter space is forbidden. It corresponds to the regions where the free-streaming and self-damping scales are above $100 kpc$ (i.e.$\sim 10^8 M_\odot$) scale. This is seen to provide a constraint involving both the interaction rate and the mass. The indications in this figure are schematic. Some factors in general of order unity are omitted for simplicity. The reader interested by these constraints should use the expressions in the text, where all factors are given explicitly.
• Figure 2: Bounds in the [Dark Matter particles' mass, Dark Matter-neutrino interaction rate] parameter space obtained from neutrino induced-damping in the URFO scenario. The Regions A, B and C are distinguished by different colors. They correspond to different expressions, given in the text, of the neutrino contribution to the Dark Matter damping length. The dot-dashed lines separate the domains according to the ordering of the epoch of the Dark Matter - neutrino decoupling, the non-relativistic transition and equality of the energy-densities. The hatches indicate in which part of the parameter space the neutrino induced-damping scale is greater than $100 kpc$ ($\sim 10^8 M_\odot$) scale. The indications in this figure are schematic. Some factors in general of order unity are omitted for simplicity. The reader interested by these constraints should use the expressions in the text, where all factors are given explicitly.
• Figure 3: Bounds in the [Dark Matter particles' mass, Dark Matter-neutrino cross-section] parameter space obtained from neutrino induced-damping in the URFO scenario. The Regions A, B and C are distinguished by different colorings. They correspond to different expressions, given in the text, of the neutrino contribution to the Dark Matter damping length. The dot-dashed lines separate the domains in the parameter space where the ordering of the Dark Matter - neutrino decoupling, the non-relativistic transition, the epoch of equality of the energy-densities changes. The hatches indicate the region in parameter space which is forbidden because the neutrino induced-damping yields damping above $100 kpc$ ($\sim 10^8 M_\odot$) scale. The indications in this figure are schematic. Some factors in general of order unity are omitted for simplicity. The reader interested by these constraints should use the expressions in the text, where all factors are given explicitly.
• Figure 4: Bounds in the [Dark Matter particles' mass, Dark Matter-neutrino interaction rate] parameter space obtained from neutrino induced-damping in the NRFO scenario. The Regions A, B and C are distinguished by different colorings. They correspond to different expressions, given in the text, of the neutrino contribution to the Dark Matter damping length. The dot-dashed lines separate the domains in the parameter space where the ordering of the Dark Matter - neutrino decoupling, the non-relativistic transition, the epoch of equality of the energy-densities changes. The hatches indicate the region in parameter space which is forbidden because the neutrino induced-damping yields damping above the $100 kpc$ ($\sim 10^8 M_\odot$) scale. The indications in this figure are schematic. Some factors in general of order unity are omitted for simplicity. The reader interested by these constraints should use the expressions in the text, where all factors are given explicitly.
• Figure 5: Bounds in the [Dark Matter particles' mass, Dark Matter-neutrino cross-section] parameter space obtained from neutrino induced-damping in the NRFO scenario. The Regions A, B and C are distinguished by different colorings. They correspond to different expressions, given in the text, of the neutrino contribution to the Dark Matter damping length. The dot-dashed lines separate the domains in the parameter space where the ordering of the Dark Matter - neutrino decoupling, the non-relativistic transition, the epoch of equality of the energy-densities changes. The hatches indicate the region in parameter space which is forbidden because the neutrino induced-damping yields damping above the $100 kpc$ ($\sim 10^8 M_\odot$) scale. The indications in this figure are schematic. Some factors in general of order unity are omitted for simplicity. The reader interested by these constraints should use the expressions in the text, where all factors are given explicitly.