Interacting Early Dark Sector

• Interacting Early Dark Sector is a class of cosmological models where non-gravitational couplings among dark energy, dark matter, and radiation modify the Universe’s pre-recombination dynamics.
• The models feature mechanisms such as disformal couplings, exponential scalar–radiation interactions, and tightly coupled dark fluids that alter the expansion history and growth of perturbations.
• Observable signatures include changes in the sound horizon, modifications in the CMB anisotropy spectrum, and potential alleviation of H0 and σ8 tensions via coupling-induced friction effects.

Searching arXiv for recent work on interacting early dark sector and closely related models. arXiv search query: "interacting early dark sector early dark energy dark matter coupling" Interacting Early Dark Sector denotes a class of cosmological scenarios in which non-gravitational interactions among dark-energy, dark-matter, dark-radiation, or early-dark-energy degrees of freedom modify the pre-recombination evolution of the Universe. In the models summarized here, the interaction can appear as a field-theoretic disformal coupling between dark energy and dark matter, an exponential coupling between a scalar and radiation, a tightly coupled interacting-dark-matter plus dark-radiation fluid that decouples during the cosmic microwave background epoch, or a phenomenological energy-transfer term introduced directly in the continuity equations (Bansal et al., 23 Aug 2025, Bisabr, 12 Feb 2025, Buen-Abad et al., 2024, Yashiki, 29 May 2025). The common theme is that the early expansion history, the sound horizon, and the growth of perturbations are altered by exchange terms or by coupling-induced friction effects rather than by a strictly noninteracting dark sector.

1. Conceptual scope and model classes

The term encompasses several distinct constructions. One class derives the interaction from a covariant action and then studies the resulting Einstein-frame dynamics. In the disformal dark-sector model, a canonical dark-energy scalar $\phi$ and a dark-matter field $\chi$ are related by a disformal metric transformation, and the pure-disformal choice is obtained by setting $C(\phi,X)=1$ and $D(\phi,X)=d_0=\text{constant}$ (Bansal et al., 23 Aug 2025). A second class couples a minimally coupled scalar representing early dark energy directly to radiation through an exponential function $C(\phi)=e^{-\xi\phi}$, which changes the radiation scaling law to $\rho_\gamma\propto a^{-4+\epsilon}$ (Bisabr, 12 Feb 2025). A third class introduces a dark atomic subcomponent of dark matter interacting with self-interacting dark radiation, so that the two form a tightly coupled fluid before dark recombination and then decouple during the CMB epoch (Buen-Abad et al., 2024). A fourth class combines a conventional axion-like EDE sector with a phenomenological interacting dark-energy–dark-matter fluid specified by $Q=\xi H\rho_{de}$ (Yashiki, 29 May 2025).

A related formal issue is whether an interaction current written in fluid form can be embedded in field theory. For the $f(R,\chi)$ framework mapped to an Einstein-frame two-scalar system, the unique field-derived interaction is

$Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$

or in FRW splitting,

$Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$

and the one-to-one mapping between fields and fluids exists only for this form up to first order in perturbations (Johnson et al., 2020). The same work classifies phenomenological interacting models into Category I, which are field-derivable, and Category II, which are phenomenological-only (Johnson et al., 2020).

A complementary fluid-based construction treats dark energy, dark matter, and dark radiation as three interacting components in a spatially flat FRW universe and introduces a three-dimensional internal space for the interaction vector $\chi$0. The “linear transversal interaction” is defined by $\chi$1, equivalently $\chi$2, and leads to a third-order source equation for the total energy density (Chimento et al., 2014).

Model class	Defining interaction	Reported early-time behavior
Pure disformal DE–DM (Bansal et al., 23 Aug 2025)	$\chi$3, $\chi$4	constant-$\chi$5 phase, then $\chi$6 dilution, then potential domination
Interacting EDE–radiation (Bisabr, 12 Feb 2025)	$\chi$7, $\chi$8	$\chi$9 and $C(\phi,X)=1$0
nuADaM (Buen-Abad et al., 2024)	iDM tightly coupled to DR	acoustic phase before dark recombination, DAO after decoupling
Mixed EDE+iDEDM (Yashiki, 29 May 2025)	$C(\phi,X)=1$1 with axion-like EDE	EDE raises $C(\phi,X)=1$2, iDEDM suppresses growth
Transversal three-fluid sector (Chimento et al., 2014)	$C(\phi,X)=1$3	effective early dark energy in Model II

2. Field-theoretic realizations and background evolution

In the pure-disformal model, the starting point is a Jordan-frame action with two scalar fields, followed by the disformal transformation

$C(\phi,X)=1$4

with $C(\phi,X)=1$5. After imposing the transformation constraint and specializing to $C(\phi,X)=1$6, $C(\phi,X)=1$7, the Einstein-frame theory contains a canonical dark-energy scalar with $C(\phi,X)=1$8, while the interaction with dark matter appears through the exchange current $C(\phi,X)=1$9 rather than through a direct modification of $D(\phi,X)=d_0=\text{constant}$0 or $D(\phi,X)=d_0=\text{constant}$1 (Bansal et al., 23 Aug 2025). In a flat FLRW background,

$D(\phi,X)=d_0=\text{constant}$2

and the scalar equation can be rewritten as

$D(\phi,X)=d_0=\text{constant}$3

with

$D(\phi,X)=d_0=\text{constant}$4

At very early times, $D(\phi,X)=d_0=\text{constant}$5 suppresses Hubble friction, so $D(\phi,X)=d_0=\text{constant}$6, hence $D(\phi,X)=d_0=\text{constant}$7 and $D(\phi,X)=d_0=\text{constant}$8. The paper describes this stage as a “kinetic-driven cosmological constant,” followed by a free-scalar phase with $D(\phi,X)=d_0=\text{constant}$9 and $C(\phi)=e^{-\xi\phi}$0 once ordinary Hubble drag is restored, and finally a late-time potential-dominated epoch (Bansal et al., 23 Aug 2025).

The transition redshift is set by

$C(\phi)=e^{-\xi\phi}$1

The reported viable range is $C(\phi)=e^{-\xi\phi}$2–$C(\phi)=e^{-\xi\phi}$3. The explicit example given is that for $C(\phi)=e^{-\xi\phi}$4 and $C(\phi)=e^{-\xi\phi}$5 one obtains $C(\phi)=e^{-\xi\phi}$6 (Bansal et al., 23 Aug 2025).

A different field-theoretic realization couples a canonical scalar to the radiation Lagrangian through

$C(\phi)=e^{-\xi\phi}$7

The coupled continuity equations are

$C(\phi)=e^{-\xi\phi}$8

with

$C(\phi)=e^{-\xi\phi}$9

If the effective transfer exponent $\rho_\gamma\propto a^{-4+\epsilon}$0 is constant, then

$\rho_\gamma\propto a^{-4+\epsilon}$1

The ratio $\rho_\gamma\propto a^{-4+\epsilon}$2 obeys

$\rho_\gamma\propto a^{-4+\epsilon}$3

and the condition $\rho_\gamma\propto a^{-4+\epsilon}$4 guarantees that $\rho_\gamma\propto a^{-4+\epsilon}$5 decreases as the Universe expands (Bisabr, 12 Feb 2025).

3. Fluid descriptions, mapping, and autonomous dynamics

The field–fluid correspondence is central to interacting early dark sector model building. In the Einstein-frame two-scalar system derived from $\rho_\gamma\propto a^{-4+\epsilon}$6, substituting the fluid expressions for $\rho_\gamma\propto a^{-4+\epsilon}$7 and $\rho_\gamma\propto a^{-4+\epsilon}$8 into the FRW equations exactly reproduces the scalar-field equations only for the field-derived interaction $\rho_\gamma\propto a^{-4+\epsilon}$9. At first order, the same uniqueness persists: the perturbative fluid equations reduce precisely to the linearized field equations only when $Q=\xi H\rho_{de}$0 is the one implied by the field theory (Johnson et al., 2020). This result constrains the admissible phenomenological interaction terms if a covariant scalar-field completion is required.

The same framework admits an autonomous-system formulation in terms of

$Q=\xi H\rho_{de}$1

with interaction strength

$Q=\xi H\rho_{de}$2

For constant $Q=\xi H\rho_{de}$3 and linear coupling, the fixed points include radiation, matter-analogue, and $Q=\xi H\rho_{de}$4-dominated solutions; the standard sequence is $Q=\xi H\rho_{de}$5. For varying $Q=\xi H\rho_{de}$6 and $Q=\xi H\rho_{de}$7, the corresponding attractors include $Q=\xi H\rho_{de}$8-dominated points with $Q=\xi H\rho_{de}$9 (Johnson et al., 2020). In the explicit example

$f(R,\chi)$0

the interacting models with $f(R,\chi)$1 enter dark-energy domination earlier than the noninteracting case. The reported crossing of $f(R,\chi)$2 over $f(R,\chi)$3 occurs at $f(R,\chi)$4 for $f(R,\chi)$5 and at $f(R,\chi)$6 for $f(R,\chi)$7, implying a shift $f(R,\chi)$8 (Johnson et al., 2020).

The multicomponent transversal-interaction model provides a separate fluid realization. The total density satisfies

$f(R,\chi)$9

and for a linear functional $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$0 the solution is

$Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$1

Its Model II splits a scalar field into vacuum-like and stiff components and imposes

$Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$2

which changes the Klein–Gordon equation to

$Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$3

For this model, the reported value is $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$4 (Chimento et al., 2014).

4. Perturbation dynamics and observable signatures

In the pure-disformal DE–DM model, linear perturbations in Newtonian gauge obey modified dark-matter continuity and Euler equations. Because $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$5 for $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$6 and $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$7, both energy-exchange and momentum-exchange terms are present, and the Euler equation contains a momentum source proportional to $Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$8 (Bansal et al., 23 Aug 2025). The reported phenomenology is scale dependent. Modes entering the horizon during the constant-$Q_\nu^{(F)} = T^{(m)}\nabla_\nu \alpha(\phi),$9 phase experience reduced friction and enhanced early growth on small scales, whereas modes entering after the transition to $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$0 feel extra drag and show suppressed growth on larger scales. The net effect can either raise or lower $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$1, depending on $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$2 and $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$3. In the CMB temperature spectrum, the late Integrated Sachs–Wolfe contribution is modified, and the model predicts a suppression of TT power at $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$4 by approximately $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$5–$Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$6 (Bansal et al., 23 Aug 2025).

The nuADaM construction realizes a different perturbative mechanism. Before dark recombination, the interacting dark matter subcomponent and dark radiation form a tightly coupled fluid governed by coupled density and velocity equations in conformal Newtonian gauge, with momentum-exchange rate $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$7 and decoupling criterion

$Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$8

For benchmark $Q=-\alpha_{,\phi}\dot\phi(\rho_m-3p_m),$9, $\chi$00, and $\chi$01, the reported ranges are $\chi$02–$\chi$03 and $\chi$04 (Buen-Abad et al., 2024). Modes entering the horizon before decoupling undergo dark acoustic oscillations, leaving a step-like suppression and residual oscillations in the matter power spectrum at

$\chi$05

In the CMB, the same dynamics produces a scale-dependent step in TT and EE, with mild high-$\chi$06 peak shifts and extra damping (Buen-Abad et al., 2024).

The interacting scalar–radiation model alters observables through a modified radiation dilution law. Because $\chi$07 for $\chi$08, the radiation density at recombination is enhanced relative to $\chi$09CDM, and the comoving sound horizon

$\chi$10

is reduced by $\chi$11 in the approximate argument given in the paper (Bisabr, 12 Feb 2025).

5. Cosmological tensions and quantitative performance

A principal motivation for interacting early dark sector models is the joint treatment of the $\chi$12, $\chi$13 or $\chi$14, and low-$\chi$15 CMB anomalies. In the pure-disformal scenario, if $\chi$16–$\chi$17, the extra early-time dark-energy density raises the expansion rate around last scattering and can increase the CMB-inferred Hubble constant by $\chi$18–$\chi$19. The same framework can slightly lower $\chi$20 and suppress low-$\chi$21 TT power by $\chi$22–$\chi$23 (Bansal et al., 23 Aug 2025).

The strongest quantitative fit improvement in the material summarized here is reported for nuADaM. Using Planck 2018 TT,TE,EE+lensing+BAO+Pantheon, plus SH0ES and EFTofBOSS in some combinations, the fit improvements relative to $\chi$24CDM+SIDR are quoted as $\chi$25 for D only, $\chi$26 for D+H, $\chi$27 for D+F, and $\chi$28 for D+H+F (Buen-Abad et al., 2024). For D+H+F, the reported marginalized values are

$\chi$29

For D+H alone, the corresponding numbers are $\chi$30, $\chi$31, $\chi$32, and $\chi$33 (Buen-Abad et al., 2024).

By contrast, the mixed EDE+iDEDM model delivers only partial relief. In the combined Planck 2018 + DESI + DES + Pantheon+ + SH0ES analysis, the reported mixed-model constraints are

$\chi$34

compared with $\chi$35 for EDE-only and $\chi$36 for iDEDM-only (Yashiki, 29 May 2025). The paper attributes the limited improvement to the fact that both EDE and iDEDM favor a higher present-day matter density, which tightens the CMB angular-scale constraint.

The interacting EDE–radiation model is presented more analytically than through a global likelihood fit. The paper states that current CMB+BAO+LSS fits require $\chi$37, and that obtaining $\chi$38–$\chi$39 with $\chi$40 and $\chi$41 early requires $\chi$42–$\chi$43 for reasonable $\chi$44 (Bisabr, 12 Feb 2025).

6. Constraints, misconceptions, and open problems

A recurring misconception is that any interacting dark-sector continuity equation can be interpreted as a consistent field theory. The field–fluid mapping analysis explicitly argues otherwise: up to first order in perturbations, the one-to-one correspondence exists only for the unique interaction current $\chi$45 (Johnson et al., 2020). This does not rule out phenomenological models, but it does separate field-derivable interactions from purely effective parameterizations.

A second misconception is that interacting early dark sector models are equivalent to conventional EDE. The pure-disformal model emphasizes the opposite point: its EDE-like behavior is produced by coupling-induced suppression of Hubble friction and by dark-matter dilution, rather than by a finely tuned scalar potential (Bansal et al., 23 Aug 2025). Similarly, nuADaM does not realize EDE through a scalar plateau at all; instead it uses a subcomponent of dark matter tightly coupled to fluid-like dark radiation until decoupling during the CMB epoch (Buen-Abad et al., 2024).

The observational status is mixed. The transversal three-component Model II gives $\chi$46, which the summary states is below older bounds $\chi$47 but slightly above the Planck+WP+highL limit $\chi$48 (Chimento et al., 2014). The mixed EDE+iDEDM model shows that combining two individually motivated ingredients does not automatically yield a simultaneous resolution of the $\chi$49 and $\chi$50 tensions (Yashiki, 29 May 2025). These results suggest that viability depends not only on raising the pre-recombination expansion rate, but also on the detailed perturbation response, the matter-density shift, and the preservation of the acoustic-scale fit.

Future tests stated in the literature include next-generation cosmological surveys and gravitational-wave observations for the disformal model (Bansal et al., 23 Aug 2025), CMB-S4, LiteBIRD, DESI full-shape clustering, Euclid, weak-lensing surveys, and Planck NPIPE reanalysis for mixed EDE+iDEDM (Yashiki, 29 May 2025), and CMBPol forecasts with $\chi$51 for early-dark-energy fractions in multicomponent interacting sectors (Chimento et al., 2014). A plausible implication is that the interacting early dark sector is best regarded not as a single model, but as a tightly constrained family of mechanisms in which the detailed form of the interaction current, the decoupling epoch, and the perturbative momentum transfer are as important as the background energy budget itself.