Mixed Dark Matter Scenarios

Updated 2 September 2025

Mixed Dark Matter is defined as cosmological models featuring multiple dark sector components with distinct microphysics that reconcile large-scale CDM success with small-scale anomalies.
The framework employs a self-regulation mechanism via oppositely-coupled dark matter species, ensuring that even strong microscopic interactions are screened in the background evolution.
MDM scenarios predict unique signatures in structure formation, including the emergence of isocurvature modes and modified halo dynamics due to attractive and repulsive scalar-mediated fifth forces.

Mixed Dark Matter (MDM) scenarios are cosmological models in which the dark matter sector is made up of two or more distinct fundamental components, each with different microphysical properties. Early motivations for MDM included reconciling the success of cold dark matter (CDM) on large scales with observational anomalies at small scales and providing a broader dark sector consistent with particle physics and cosmological constraints. MDM frameworks accommodate both species that behave as cold (collisionless, pressureless) dark matter and those that exhibit significant free-streaming or interactions—including warm/hot relics, axion-like particles, or dark matter coupled to dark energy—leading to rich phenomenology in structure formation, cosmic microwave background (CMB) signatures, and potential new signatures in non-gravitational searches.

1. Theoretical Construction: Composition and Self-Regulation

MDM models posit the existence of multiple dark sector particles, realized as coexisting fluids or fields with distinct interactions or mass scales. A cornerstone example is the coupled dark energy model with two CDM species (“+” and “–”) of identical intrinsic properties, differing only by the sign of their coupling to a quintessence-like scalar field $\phi$ (Baldi, 2012). Each species experiences a coupling $C = \sqrt{2/3}~\beta/M_\mathrm{Pl}$ , with equal-magnitude but opposite sign. The scalar–dark matter Lagrangian density thereby includes interaction terms $+\beta$ and $-\beta$ for the respective species.

The model’s evolution is dictated by a set of background equations:

Scalar field: $\ddot{\phi} + 3H \dot{\phi} + V_{,\phi} = +C\rho_{+} - C\rho_{-}$
Conservation for each CDM species:

$\dot{\rho}_{+} + 3H\rho_{+} = -C\dot{\phi}\rho_{+},\qquad \dot{\rho}_{-} + 3H\rho_{-} = +C\dot{\phi}\rho_{-}$

Evolution of mass: $\frac{d\ln(M_{\pm}/M_\mathrm{Pl})}{dt} = \mp C\dot{\phi}$

Introducing a dimensionless asymmetry $\mu = (\Omega_{+} - \Omega_{-})/(\Omega_{+} + \Omega_{-})$ , the effective coupling to the background becomes $\beta_\mathrm{eff} = \beta\mu$ . Importantly, early-universe evolution tends to dynamically drive $\mu \rightarrow 0$ during matter domination, resulting in the self-regulation of effective coupling: even when the microscopic coupling $\beta$ is large, the net effect on background expansion is screened. This ensures that the homogeneous cosmology tracks $\Lambda$ CDM closely, contrasting with single-component coupled dark matter—where even small $\beta$ values are observationally excluded due to distortions in the background evolution (Baldi, 2012).

2. Linear Perturbation Theory and Fifth-Force Dynamics

Linear structure growth in MDM scenarios deviates sharply from both the standard CDM case and single-species coupled models. For two-component models with opposite DE couplings, the density contrasts $\delta_{+}$ and $\delta_{-}$ evolve as: $\ddot{\delta}_{+} = -2H\left[1 - {\beta \dot{\phi}}\big/(H\sqrt{6})\right]\dot{\delta}_{+} + 4\pi G\left[\rho_{+}\delta_{+}\Gamma_A + \rho_{-}\delta_{-}\Gamma_R\right]$

$\ddot{\delta}_{-} = -2H\left[1 + {\beta \dot{\phi}}\big/(H\sqrt{6})\right]\dot{\delta}_{-} + 4\pi G\left[\rho_{-}\delta_{-}\Gamma_A + \rho_{+}\delta_{+}\Gamma_R\right]$

with $\Gamma_A = 1 + (4/3)\beta^2$ (enhanced “attractive” force within species) and $\Gamma_R = 1 - (4/3)\beta^2$ (“repulsive” cross-species term).

Notably, for adiabatic initial conditions (equal fractional fluctuations in both species), the attractive and repulsive corrections nearly cancel. However, the “friction” terms, with opposite signs, gradually drive isocurvature between the species, leading to a breakdown of adiabaticity and the emergence of isocurvature modes. For isocurvature initial conditions, the usual gravitational source cancels, and the repulsive or attractive fifth-force dominates, causing growth or decay of relative perturbations.

For large $\beta$ , the linear growth factor and present-day $\sigma_8$ can be strongly boosted, leading to a late-time structure amplitude in conflict with observations; for moderate $\beta \lesssim 1$ , the deviations remain small. In contrast to single-coupled dark matter, where even $\beta \sim 0.1$ is excluded, MDM with this self-cancellation mechanism allows $\beta \sim 1$ without violating linear structure constraints (Baldi, 2012).

3. Non-Standard Structure Formation: Isocurvature Growth and Fifth Forces

A key feature of these MDM models is the emergence of new long-range scalar forces mediated by the dark energy field. The intra-species fifth force is always attractive and can be as strong as or stronger than gravity for $\beta \gtrsim 1$ . The cross-species fifth-force can become repulsive (for $\beta > \sqrt{3}/2$ ), resulting in possible suppression of cross-species correlations and a net repulsion.

The most distinctive prediction is the dynamical evolution toward isocurvature: initially adiabatic perturbations are driven quantitatively toward isocurvature by the friction (momentum-exchange) asymmetry. The net effect is a distinct perturbative evolution, potentially differentiable from single-fluid scenarios through precision measurement of isocurvature and total matter perturbation evolution, e.g.,

$\delta_\mathrm{CDM} = \frac{\Omega_{+}\delta_{+} + \Omega_{-}\delta_{-}}{\Omega_{+} + \Omega_{-}}$

Numerical integration of these equations confirms strong departures from $\Lambda$ CDM for extreme $\beta$ , but with observational viability for $\beta \lesssim 1$ , and complete compatibility in background expansion even for much larger $\beta$ if $\mu\to0$ is maintained (Baldi, 2012).

4. Comparison with Alternative MDM Scenarios and Observational Signatures

In alternative realizations, the “mixed” structure arises from combining particles with distinct free-streaming or thermal properties (e.g., warm and cold dark matter, WDM+CDM, or neutrino/axion admixtures). In these regimes, the suppression of small-scale clustering and halo substructure is regulated by the free-streaming scale of the “hot” or “warm” component, while the “cold” component retains bottom-up clustering (Harada et al., 2014, Parimbelli et al., 2021, Dome et al., 17 Sep 2024). The distinguishing signatures for the self-coupled, “charge-like” MDM scenario are:

Screening of background signatures even for order-one couplings due to self-regulation;
The appearance of long-range scalar-mediated forces (attractive or repulsive) at linear and potentially non-linear scales;
The selective enhancement or suppression of structure growth, governed by both $\beta$ and the asymmetry $\mu$ , together with a unique evolution from adiabatic toward isocurvature modes.

This contrasts with thermally-mixed MDM, where the key signatures are scale-dependent structure suppression and subhalo abundance reduction—without a fifth-force mediation—so observational strategies must focus accordingly. In all non-CDM MDM scenarios, constraints from CMB, galaxy clustering, lensing, and halo mass function measurements are applicable, but the interplay of model parameters (e.g., $\beta$ , $\mu$ , $r_\mathrm{WDM}$ ) must be accounted for to interpret limits (Kamada et al., 2016, Tan et al., 27 Sep 2024, Inoue et al., 2023).

5. Theoretical and Experimental Constraints

Observational consequences arise predominantly from:

Background cosmological expansion, where the self-regulation mechanism ensures effective screening for the background (i.e., $\beta_\mathrm{eff}\rightarrow 0$ );
Linear and non-linear perturbation growth, where large $\beta$ values can enhance structure growth ( $\sigma_8$ ), generate isocurvature, and impact halo abundance;
New “fifth-force” effects that could be probed in contexts sensitive to small-scale structure or via possible indirect detection in the case that the quartic couplings produce unusual nonlinearities.

Current large-scale structure, CMB, and lensing data provide lower and upper bounds on $\beta$ , with the model viable for $\beta\lesssim 1$ and $\mu\ll 1$ , but ruled out for $\beta \gtrsim 1.6$ as the enhancement in $\sigma_8$ outpaces observationally allowed levels (Baldi, 2012). The mechanism is thus distinct among MDM scenarios: whereas single-species coupled dark matter is tightly restricted, this MDM “charge-coupled” scenario allows for strong microscopic interactions without disrupting the standard cosmological background.

6. Broader Implications and Prospective Probes

MDM scenarios with self-regulation provide a theoretically motivated resolution to the tension between possible strong dark sector interactions and stringent cosmological bounds. The interplay of adiabatic/isocurvature dynamics and the presence of non-gravitational long-range forces provides a cosmological “laboratory” to seek departures from single-component, collisionless dark matter prescriptions. Precision probes of the large- and small-scale matter power spectrum, isocurvature fraction (e.g., future CMB polarization), and studies of halo abundance and structure formation offers the best opportunity to distinguish such models from CDM and other MDM frameworks.

Further, N-body simulations capable of resolving the perturbative and nonlinear impact of these fifth-force and asymmetry-driven mechanisms are required for future testing. In addition, comparative studies to alternative multi-component models—especially those featuring warm/hot relics, subdominant interacting sectors, or scalar field interactions—will be essential for discriminating the unique phenomenology of self-regulated, charge-coupled MDM.

In summary, Multiple Dark Matter scenarios with oppositely-coupled dark sector species provide a mechanism whereby large dark sector interactions are possible due to self-screening at the background level. The remaining cosmological and astrophysical effects—emergence of long-range scalar forces, distinctive perturbative evolution toward isocurvature, and regulated growth of structure—provide sharp targets both for theoretical analysis and for future empirical constraints (Baldi, 2012).