Interacting Dark Matter and Dark Energy

• Interacting dark energy (IDE) models introduce non-gravitational energy and momentum exchange between dark matter and dark energy, altering both the expansion history and growth of cosmic structures.
• Phenomenological formulations employ coupling kernels such as Q ∝ H(λₑρ_de + λ_χρ_χ) to adjust dark sector dynamics and address issues like the coincidence problem and cosmic tension.
• Observational constraints from CMB, BAO, SNe, and weak lensing, alongside N-body simulations, tightly bound IDE parameters and refine expectations for nonlinear structure formation.

Interactions between dark matter (DM) and dark energy (DE)—collectively termed Interacting Dark Energy (IDE)—constitute a class of cosmological models in which non-gravitational energy and momentum exchange modifies the canonical ΛCDM background and structure-formation dynamics. IDE frameworks arise from the recognition that, while the total stress–energy tensor must be covariantly conserved, the division between dark sector components is arbitrary and may admit coupling terms that alter both the expansion history and growth of perturbations. IDE models are motivated by issues such as the coincidence problem, tensions in cosmic parameter measurements, and the search for nontrivial dark sector phenomenology distinct from ΛCDM.

1. Phenomenological and Theoretical Formulations of IDE

The standard formalism of IDE introduces an interaction kernel $Q$ in the coupled continuity equations for the DM and DE fluids (taking $8\pi G=1$ units except where specified): $$\begin{align*} &\dot\rho_\chi + 3H\rho_\chi = Q, \ &\dot\rho_{\rm de} + 3H(1+w_{\rm de})\rho_{\rm de} + 9H^2\zeta = -Q, \end{align*}$$ where $\rho_\chi$ and $\rho_{\rm de}$ are the energy densities of DM and DE, $w_{\rm de}$ is the DE equation of state, $H$ is the Hubble parameter, and $\zeta$ quantifies the bulk viscosity of the DE fluid in viscous dark energy (VDE) scenarios (Halder et al., 2024, Tamanini, 2015).

A widely studied generalization of $Q$ is

$$Q = 3H(\lambda_e \rho_{\rm de} + \lambda_\chi \rho_\chi).$$

By parametric choices of $\lambda_\chi, \lambda_e$, canonical benchmarks are recovered:

• $Q=3\lambda_{\rm de}H\rho_{\rm de}$ (pure dark energy coupling),
• $Q=3\lambda_\chi H\rho_\chi$ (pure dark matter coupling),
• $Q=3\lambda H(\rho_\chi+\rho_{\rm de})$ (symmetric coupling).

Alternative parametrizations use nonlinear or sign-changing forms, such as $Q \propto \rho_{\rm de}\rho_\chi$, or time-varying couplings $\beta(a)$ allowing reversal of energy flow during cosmic evolution (Li et al., 13 Jan 2025, Westhuizen et al., 1 Sep 2025, Escobal et al., 9 Jan 2026). Field-theoretic models realize $Q$ via interactions in scalar–tensor, axion or disformal gravity scenarios.

2. Impact on Background Evolution and Observational Diagnostics

The coupled continuity equations, together with the Friedmann constraint,

$$H^2 = \frac{1}{3}(\rho_b + \rho_{\rm rad} + \rho_\chi + \rho_{\rm de}),$$

result in altered scaling laws for $\rho_\chi(a), \rho_{\rm de}(a)$ and deviations in $H(z)$. For linear kernels, analytic solutions exhibit modified exponents in the scale factor; e.g., for $Q=3H\lambda_{\rm de}\rho_{\rm de}$,

$$\rho_{\rm de}(a) = \rho_{{\rm de},0}\, a^{-3(1 + w_{\rm de}) - 3\lambda_{\rm de}},$$

and for $Q=3H\lambda_\chi\rho_\chi$,

$\rho_\chi(a) \propto a^{-3 + 3\lambda_\chi}.$

These modifications propagate into derived observables such as distance–redshift relations, cosmic chronometer $H(z)$ points, and growth-rate measures.

Bulk viscosity introduces an additional effective pressure, $$p_{\rm de}^{\rm eff}=w_{\rm de}\rho_{\rm de} - 3\zeta H$$, impacting both the acceleration parameter $q(z)$ and higher cosmographic diagnostics (jerk $j(z)$, snap $s(z)$), as elucidated in the VDE+IDE framework (Halder et al., 2024).

Statefinder ($r$, $s$), Om diagnostics, and derived tracks in the $(\Omega_{\rm de}, \Omega_m)$ plane provide quantitative probes of deviations from ΛCDM, sensitive to the coupling parameters and viscosity (Westhuizen et al., 1 Sep 2025, Halder et al., 2024). For example, Om$(z)$, which is constant for ΛCDM, exhibits phantom- or quintessence-like signatures in IDE+VDE models, while Om3 discriminates dynamic DE.

3. Structure Formation, Linear Growth, and Nonlinear Evolution

IDE modifies both linear and nonlinear structure-formation processes. The linear growth of matter perturbations $\delta_\chi$ is governed by

$$\ddot{\delta}_\chi + [2H + Q/\rho_\chi]\dot{\delta}_\chi - 4\pi G_{\rm eff}\rho_\chi\delta_\chi = 0,$$

with an effective Newton constant $G_{\rm eff}$ influenced by $Q$ (Wang et al., 2016, Liu et al., 2022, Pooya, 2024).

Nonlinear simulations using N-body codes adapted to evolving particle masses, velocity-dependent friction, and time-varying expansion histories demonstrate that the interaction parameter sensitively affects halo mass accretion, internal density structure, concentration–mass relation, spin, and shape distributions (Liu et al., 2022, Zhao et al., 7 Jan 2025):

IDE Model	Halo Mass Growth	Concentration–Mass	Spin–Tidal Alignment
DM $\to$ DE	Suppressed, may lose mass at late times	Systematically lower ($R\sim 0.4$ for $\xi<0$)	Shape–tidal enhanced; spin–tidal suppressed
DE $\to$ DM	Enhanced at late times	Systematically higher ($R\sim 1.5$ for $\xi>0$)	Shape–tidal suppressed; spin–tidal enhanced

Precise constraints can be placed by exploiting the mass-independence of the concentration shift: $$\ln(c_{\rm IDE}/c_{\Lambda{\rm CDM}}) \sim \alpha\xi_2$$ with $\alpha\simeq 8$ (Liu et al., 2022). Any significant IDE-induced suppression or enhancement is already tightly limited by observed cluster abundances and weak lensing.

At the mildly nonlinear level, one-loop corrections to the matter power spectrum in the EFTofLSS formalism have been computed. A nonlinear coupling, $Q = \Gamma \rho_m \rho_{\rm DE} \theta_m$, affects only the nonlinear mode-coupling kernel, and the current bounds indicate $|\Gamma| \lesssim 0.01$ from BOSS full-shape power spectrum fits (Silva et al., 12 Dec 2025).

4. Theoretical and Observational Constraints on Interaction Parameters

Multiple lines of evidence converge to confine IDE couplings to small absolute values:

• For linear $Q \propto H\rho},$ $|\xi| \lesssim 0.01$–0.1 at 68–95% CL from combined Planck, BAO, SNe, RSD, and lensing datasets (Wang et al., 2016, Wang et al., 2024, Ghedini et al., 2024, Giarè et al., 2024).
• Nonlinear and sign-changing kernels admit somewhat larger couplings in carefully chosen regimes, but positivity of densities and no–Big Rip requirements limit viable parameter space (Westhuizen et al., 1 Sep 2025, Westhuizen et al., 1 Sep 2025, Li et al., 13 Jan 2025).
• New microphysical models where $Q\propto\rho^2$ (motivated by Boltzmann-equation annihilation/creation) find the DM self-annihilation cross section per unit mass must be suppressed at least to $A < 7.6\times 10^{-25}$ (dimensionless), while DE self-annihilation is less tightly constrained, $B<0.048$ (95% CL) (Escobal et al., 9 Jan 2026).

Current cosmological datasets (Planck CMB, BAO, Pantheon+, DESI, cosmic chronometers, RSD, SNIa) together leave little room for nonzero $Q$ at even the percent level. These constraints are further “cornered” by the inclusion of redshift-space distortion data, which tightly bind the growth rate $f\sigma_8(z)$ to ΛCDM values (Ghedini et al., 2024).

Bayesian evidence generally does not favor IDE over ΛCDM, but in cases with sign-changing $Q$—specifically, those where $\beta(z)$ crosses zero at $z\sim 1$ and the direction of energy flow reverses—modest preference is seen (Li et al., 13 Jan 2025).

5. Pathologies, Theoretical Viability, and Model Selection

Three principal theoretical issues emerge in the dynamical system analysis:

• Negativity of energy densities: Energy transfer from DM $\to$ DE ($Q<0$ for most conventions) generically drives either $\rho_{\rm de}<0$ in the past or $\rho_\chi<0$ in the future, unless coupling is minuscule. DE $\to$ DM ($Q>0$) with small coupling avoids these pathologies (Westhuizen et al., 2023, Westhuizen et al., 1 Sep 2025, Westhuizen et al., 1 Sep 2025).
• Perturbation instabilities: Naive IDE perturbation theory can develop rapid super-horizon divergences ("doom factors"), especially for $w_{\rm de}>-1$ and $Q\propto\rho_c$. Parametrized post-Friedmann (PPF) treatments regularize these instabilities and make the full parameter space accessible to MCMC analysis (Zhang, 2017).
• Big Rip singularities: Couplings that induce effective $w_{\rm eff}<-1$ asymptotically can yield scale factor blow-up in finite proper time (Big Rip). Constraints on the coupling and $w_{\rm de}$ can ensure avoidance (Westhuizen et al., 1 Sep 2025, Westhuizen et al., 2023).
• Physical consistency dictates favoring energy transfer from DE to DM (iDEDM) over the reverse, both for positivity and for alleviating the coincidence problem, with nonlinear models such as $$Q \propto \rho_\chi \rho_{\rm de}/(\rho_\chi+\rho_{\rm de})$$ being especially robust (Westhuizen et al., 1 Sep 2025).

6. IDE in Viscous Dark Energy, Unified Dark Sector, and Alternative Models

The incorporation of viscosity in the DE fluid further generalizes IDE scenarios. In the VDE+IDE scheme, the bulk-viscosity term $\zeta=\eta H$ introduces a negative pressure $-3\zeta H$, acting to decelerate cosmic expansion and modulate the competition between DE and DM. Bayesian MCMC analysis of SNIa data (Union 2.1) yields best-fit $\eta\approx 0.05$ and $\lambda_r\approx 0.09$, yielding quantifiable departures from ΛCDM at $z \gtrsim 1$—notably in $H(z)$, $\Omega_i(z)$, and higher-order cosmographic parameters ($q, j, s$) (Halder et al., 2024).

IDE has also been explored in the context of unified dark sector models embodying generalized Chaplygin gas, K-essence, or time-varying $\Lambda$ with additional interaction parameters $\Gamma$ (MV et al., 2024). Parameter dependence and functional form of the interaction determine sensitivity of observables—e.g., K-essence models are far more responsive to changes in $\Gamma$.

Alternative theories have postulated fundamentally non-phenomenological interactions, such as chaos-dominated thermodynamic exchanges between DM and DE, in which non-equilibrium dynamics yield Lyapunov-exponent positive chaos, potentially encoding new universality classes in the dark sector (Aydiner, 2023).

7. Future Directions and Multi-Probe IDE Constraints

Advances in observational capability will dramatically improve IDE tests. Stage IV galaxy surveys (DESI, Euclid, LSST), 21cm intensity mapping (SKA, BINGO), gravitational-wave standard sirens, and mass-resolved weak lensing will shrink allowed couplings to the sub-percent level and directly probe nonlinear structure signatures (Wang et al., 2024, Zhao et al., 2022). Fast radio bursts, due to their sensitivity to late-time expansion and different systematics, offer a promising probe, with $10^6$ localized events providing $|\beta| \lesssim 0.1$ constraints (Zhao et al., 2022).

N-body simulations tailored for IDE, especially regarding halo concentration–mass relations, spin–tidal alignments, and the intrinsic alignment of galaxies, will continue to drive down parameter uncertainties and sharpen theoretical selection among permissible $Q$ functional forms (Liu et al., 2022, Zhao et al., 7 Jan 2025).

---

In summary, IDE models remain a well-motivated extension of standard cosmology, with current data supporting only mild, positive couplings (DE $\to$ DM), and kinetic or viscous dark sector generalizations offering further phenomenological richness. The combined application of background, linear, and nonlinear structure growth data—anchored by robust treatments of perturbation theory and pathologies—constitutes the state of the art in constraining or discovering non-gravitational dark sector interactions (Halder et al., 2024, Westhuizen et al., 1 Sep 2025, Zhao et al., 7 Jan 2025, Wang et al., 2024, Wang et al., 2016).