---
title: Dark Radiation Matter Decoupling (DRMD)
url: https://www.emergentmind.com/topics/dark-radiation-matter-decoupling-drmd
type: topic
---

# Dark Radiation Matter Decoupling (DRMD)

Searching arXiv for the cited DRMD-related papers to ground the article in recent and relevant literature.
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arxiv_search.query({"search_query":"id:1803.03644","max_results":3,"sort_by":"relevance","sort_order":"descending"})
arxiv_search.query({"search_query":"all:\"dark radiation matter decoupling\" OR all:\"dark acoustic oscillations\"","max_results":10,"sort_by":"submittedDate","sort_order":"descending"})
Dark Radiation Matter Decoupling (DRMD) denotes a family of dark-sector cosmologies in which the relation between a non-relativistic dark-matter component and a relativistic dark-radiation component changes with time. In the narrow sense, it refers to an interacting DM–DR subsystem that is tightly coupled in the early universe and later decouples, thereby imprinting dark acoustic oscillations, collisional damping, and scale-dependent changes in the CMB and matter power spectrum. In broader phenomenological usage, closely related constructions also include post-BBN conversion of dark matter into free-streaming dark radiation, entropy transfer from matter into radiation after sector decoupling, and late decays that create a daughter species that is radiation-like at production but matter-like after redshifting. Taken together, these realizations make DRMD a unifying label for time-dependent drag, transfer, or relativistic-to-nonrelativistic transition in the dark sector [2511.16554] [1803.03644] [1303.6267].

## 1. Conceptual scope and taxonomy

The modern literature does not reduce DRMD to a single microscopic mechanism. One branch treats the problem as a perturbative transition in the radiation sector itself: dark radiation can be free-streaming, fluid, decoupling, instantaneous decoupling, or recoupling, with the distinction encoded directly in the Boltzmann hierarchy rather than in a specific UV completion [2212.13264]. In that setting, the key issue is whether the DR multipoles above the dipole are collisionally damped or freely propagated, and whether the transition occurs gradually or abruptly.

A second branch studies true DM–DR drag. In these models only a subcomponent of dark matter is interacting, while the dominant remainder stays collisionless. The interacting subcomponent and the dark radiation behave as a pressure-supported dark fluid before decoupling, and the rate and sharpness of the transition determine the amplitude and phase structure of dark acoustic oscillations [2511.16554]. A closely related ETHOS formulation parameterizes the DR–DM scattering rate directly by a temperature power law and uses that effective drag history to classify the decoupling phenomenology [1907.01496].

A third branch is not a literal scattering-decoupling calculation but an effective transfer model in which cold dark matter is converted into a non-interacting relativistic component. In this usage, DRMD is better read as a post-decoupling DM\(\to\)DR conversion history than as a coupled-fluid kinetic decoupling problem. Both the general post-BBN conversion model of Bringmann et al. and the late-universe DMDR model of Pandey et al. fall into this category [1803.03644] [2011.04606].

A fourth branch replaces interaction-driven decoupling by kinematics. In late-decay models, a heavy parent freezes out, decays after neutrino decoupling, and injects a stable daughter that behaves either as dark radiation or as warm dark matter depending on the mass ratio and lifetime. This is a radiation-to-matter transition caused by cosmological redshifting rather than by a scattering rate crossing the Hubble scale [1303.6267].

## 2. Effective transfer formalisms

The most conservative transfer description begins by relaxing the assumption that the cold-dark-matter density is covariantly conserved. Bringmann et al. parameterize the DM background as
\[
\rho_\chi (a)= \frac{\rho^0_\chi}{a^3}\left[1+ \zeta\frac{1-a^\kappa}{1 +(a/a_t)^\kappa}\right]\,,
\]
where \(\zeta\) controls the total reduction in comoving DM density, \(a_t\) sets the transition epoch, and \(\kappa\) controls the transition width. In this parameterization the comoving DM density decreases overall by a factor \(1+\zeta\); \(\kappa=2\) approximately reproduces decaying-DM-like behavior, while \(\kappa=1\) maps well to Sommerfeld-enhanced annihilation [1803.03644].

Energy conservation is imposed through
\[
\frac{d\rho_\chi}{dt}+3H\rho_\chi\equiv-\mathcal Q,\qquad
\frac{d\rho_\phi}{dt}+4H\rho_\phi=\mathcal Q,
\]
with the produced radiation taken to be non-interacting and free-streaming, “as for an additional neutrino species.” The resulting effective neutrino equivalent,
\[
\Delta \tilde N_{\rm eff}(a)=\frac{\rho_\phi(a)}{\rho_{1\nu}(a)}
=\frac87\left(\frac{11}{4}\right)^{4/3}\frac{\rho_\phi(a)}{\rho_\gamma(a)},
\]
is generically time dependent rather than constant, which is one of the central differences between DM\(\to\)DR conversion and the usual constant-\(\Delta N_{\rm eff}\) parameterization [1803.03644].

Pandey et al. adopt the same general logic for a late-universe DMDR model, but reduce the background freedom to two parameters by imposing \(1-\zeta a_t^\kappa=0\), so that the conversion accelerates toward the present epoch. Their dark-matter density is
\[
\rho_{\rm dm}(a)=\frac{\rho_{\rm dm}^0}{a^3}\left[1+\zeta\,\frac{1-a^\kappa}{1+\zeta a^\kappa}\right].
\]
Here \(\zeta\) is “the total amount of dark matter that has already converted into dark radiation, divided by the amount of dark matter at the current time,” while \(\kappa\) characterizes the conversion rate. As in the Bringmann et al. framework, the source term is defined by
\[
\frac{1}{a^3}\frac{d}{dt}(a^3 \rho_{\rm dm})
=-\frac{1}{a^4}\frac{d}{dt}(a^4 \rho_{\rm dr})
=-\mathcal Q,
\]
and the perturbative prescription is fixed by the minimal choice \(\delta\mathcal Q=\mathcal Q\,\delta_{\rm dm}\) [2011.04606].

These effective-transfer descriptions share a specific physical assumption: the created DR is a separate dark relativistic component, not an extra massless neutrino species sharing the neutrino temperature or entropy bath. That distinction matters once massive neutrinos are included and once one asks whether the product species is free-streaming, fluid-like, or still coupled to a dark bath [2011.04606].

## 3. Interaction-driven decoupling and dark acoustic oscillations

In true DRMD models, the primary object is not \(\mathcal Q\) but a momentum-exchange rate. A representative formulation splits the dark matter into a dominant non-interacting sector and an interacting subcomponent of fractional abundance
\[
f_{\rm idm}\equiv \frac{\rho_{\rm idm}}{\rho_{\rm dm}}\,.
\]
The interacting DM and dark radiation obey coupled Euler equations with drag terms,
\[
\dot{\theta}_{\rm idm}
= - \mathcal{H} \theta + c_{d,s}^2 k^2 \delta_{\rm idm} + k^2 \psi
+ S \gamma \Gamma_d ( \theta_{\rm dr} - \theta_{\rm idm} ),
\]
\[
\dot{\theta}_{\rm dr}
= \frac{1}{4}\delta_{\rm dr} + k^2 \psi
+ \gamma \Gamma_d ( \theta_{\rm idm} - \theta_{\rm dr} ),
\]
with
\[
S\equiv \frac{4\rho_{\rm dr}}{3\rho_{\rm idm}}.
\]
The drag history is parameterized by
\[
\Gamma_d(T)=\Gamma_d^0\left(\frac{T}{T_0}\right)^{2+n},
\]
with benchmark cases \(n=4\), \(n=2\), and an \(n=0\) case supplemented by an exponential shutoff, \(\Gamma_d\propto T^2 e^{-a/a_{\rm tr}}\). The preferred decoupling epoch is close to matter-radiation equality, \(\log_{10}z_{\rm dec}\approx 3.3\) [2511.16554].

When \(\Gamma_d\gg H\), the interacting DM and DR behave as a single tightly coupled fluid. Pressure support from the DR component suppresses the growth of iDM perturbations and generates dark acoustic oscillations. The sharpness of the DAO pattern is controlled by the sharpness of decoupling: fast decoupling freezes in a sharply defined oscillation phase, while slow decoupling smears the feature [2511.16554]. In the ETHOS language, the relevant drag amplitude is organized by \(a_{\rm dark}\xi^4\), where \(\xi=T_{\rm DR}/T_\gamma\), and the comoving interaction rate is written as
\[
\Gamma_{\rm DR-DM}
=-\Omega_{\rm DM}h^2\,a_{\rm dark}
\left(\frac{1+z}{1+z_d}\right)^n,\qquad z_d=10^7,
\]
with
\[
\Gamma_{\rm DM-DR}
=\left(\frac{4}{3}\frac{\rho_{\rm DR}}{\rho_{\rm DM}}\right)\Gamma_{\rm DR-DM}.
\]
For \(n=2\) and \(n=4\), this yields sharp small-scale suppression plus DAO; for \(n=0\), the suppression is smoother because the proper-time momentum-transfer rate scales as \(T^2\) and remains comparatively important near recombination [1907.01496].

A related effective description focuses on the dark-radiation perturbation sector rather than on explicit DM drag. In that language, the collision term damps the quadrupole and higher moments,
\[
\dot{F}_{2}=\frac{2k}{5}F_{1}-\frac{3k}{5}F_{3}
+\frac{4}{15}\dot h+\frac{8}{5}\dot\eta
-\alpha_2 a\langle\Gamma\rangle F_2,
\]
\[
\dot{F}_{\ell}
=\frac{k}{2\ell+1}\left[\ell F_{\ell-1}-(\ell+1)F_{\ell+1}\right]
-\alpha_\ell a\langle\Gamma\rangle F_\ell,\qquad \ell\ge3.
\]
This makes the fluid-to-free-streaming transition explicit and supports free-streaming DR, fluid DR, decoupling DR, instantaneous decoupling DR, and recoupling DR within a common relaxation-time formalism [2212.13264].

The acoustic scale associated with DRMD is the dark drag horizon,
\[
r_{d,\mathrm{DAO}}
= \int_0^{\eta_{\mathrm{dec}}} d\eta\, c_{s,\mathrm{eff}}(\eta)
= \int_{z_\mathrm{dec}}^\infty dz\, \frac{c_{s,\mathrm{eff}}(z)}{H(z)},
\]
where the tightly coupled dark fluid has effective sound speed \(c_{s,\mathrm{eff}}^2=c_s^2/(1+R)\). Using only Planck and SH0ES-calibrated supernovae, one finds evidence for a DAO signal with
\[
r_{d,\mathrm{DAO}}\in[53.7,64.8]~\mathrm{Mpc}/h,\qquad
A_{\mathrm{DAO}}=0.031^{+0.014}_{-0.011}
\]
at \(68\%\) posterior interval, with the DAO scale naturally near half the BAO scale because the preferred decoupling occurs around equality rather than baryon drag [2602.23895].

## 4. Microphysical realizations

Several explicit particle models realize DRMD or closely adjacent phenomena. One realization embeds late kinetic decoupling inside a Dirac-fermion dark sector with a light vector mediator,
\[
\mathcal L\supset g_\chi \bar\chi\gamma^\mu\chi V_\mu.
\]
After kinetic decoupling, the DM velocity redshifts as \(v\propto a^{-1}\) instead of \(a^{-1/2}\), so near a Sommerfeld resonance with \(S(v)\propto v^{-2}\), the annihilation rate per particle becomes increasingly important at late times and produces a second annihilation epoch long after chemical freeze-out. In that case, late kinetic decoupling is not itself the conversion; it is the mechanism that enables delayed annihilation into dark radiation [1803.03644].

A more direct kinetic-decoupling model uses a global \(U(1)\) dark sector with a pseudo-Dirac fermion \(\chi_-\) as DM and a massless Goldstone boson \(\eta\) as DR. The DM–DR scattering cross section is
\[
\sigma_{\eta\chi_-}
=\frac{8\pi \alpha_{\rm d}^2 \omega^4}{\Delta m_\chi^6}
\left(1+\frac{16\Delta m_\chi^2}{3m_\rho^2}
+\frac{8\Delta m_\chi^4}{m_\rho^4}\right),
\]
which leads to the kinetic-decoupling condition
\[
\left(\frac{T_\eta}{m_\chi}\right)n_\eta \sigma_{\eta\chi_-}\sim H(T_\gamma)
\]
and to the estimate
\[
T_{\rm kd}\simeq 0.5\,{\rm keV}\;
\frac{\delta}{10^{-4.5}}
\left(\frac{m_\chi}{\rm GeV}\right)^{7/6}
\left(\frac{10^{-4}}{\alpha_{\rm d}}\right)^{1/3}
\xi_{\rm kd}^{-4/3}.
\]
The associated acoustic cutoff scale is
\[
M_{\rm cut}\simeq 1.7\times10^8
\left(\frac{T_{\rm kd}}{\rm keV}\right)^{-3}M_\odot,
\]
and the preferred DM mass range is \(100~\mathrm{keV}\lesssim m_\chi\lesssim 10~\mathrm{GeV}\) [1404.6127].

A non-Abelian realization starts from a hidden \(SU(3)\) gauge theory spontaneously broken to a residual \(SU(2)\). The broken generators become massive vector dark matter, while the unbroken \(SU(2)\) gauge bosons remain massless and constitute dark radiation. Because the residual symmetry is non-Abelian, the DM–DR scattering scales as
\[
\sigma \sim \frac{g^4}{T^2},
\]
rather than the Thomson-like \(g^4/m_{\rm DM}^2\) behavior of an Abelian residual subgroup. This temperature dependence makes the drag cosmologically relevant deep into the radiation era and numerically suppresses \(\sigma_8\) relative to \(\Lambda\)CDM [1609.02307].

Another class of constructions modifies the thermal initial conditions rather than the late-time interaction law. In asymmetric-reheating models, a long-lived modulus reheats the visible and dark sectors unequally, so the dark radiation bath is cold from the outset. Achieving \(\xi\sim0.1\) requires
\[
\frac{\rho_D^{\rm RH}}{\rho_B^{\rm RH}}\sim 2.5\times10^{-4},
\]
which permits an interacting DM–DR sector while evading the overproduction of dark radiation that would follow from an earlier thermalized visible–dark history [1511.06768].

## 5. Observational constraints and tension relief

The conversion class is already tightly bounded. Bringmann et al. showed that CMB data strongly constrain any significant DM\(\to\)DR conversion after BBN. For very early transitions, the model reduces observationally to a nearly constant-\(\Delta N_{\rm eff}\) cosmology, with a frequentist bound roughly
\[
\Delta N_{\rm eff}<0.29
\]
for \(a_t=10^{-7}\) and \(\kappa=2,4\). For late conversion, CMB-only data require that the DM density not be reduced by more than a few percent after matter-radiation equality, while adding low-redshift data can allow up to around \(10\) percent of DM to be converted during matter domination and gives only a mild frequentist preference, around \(\sim 2\sigma\), for late conversion [1803.03644].

The later DMDR analysis of DES-Y1, Planck-2018, Pantheon, and BAO found no evidence for nonzero conversion. The converted fraction \(\zeta\) is constrained at \(68\%\) confidence level to be
\[
\zeta<0.32 \quad \text{(DES-Y1 3x2pt)},
\]
\[
\zeta<0.030 \quad \text{(CMB+SN+BAO)},
\]
\[
\zeta<0.037 \quad \text{(combined dataset)}.
\]
The tension in \(S_8\) is only slightly reduced, from \(2.3\sigma\) to \(1.9\sigma\), the Hubble tension remains \(3.8\sigma\), and the evidence ratio disfavors the DMDR extension relative to \(\Lambda\)CDM for the external and combined datasets [2011.04606].

For true DM–DR drag, the strongest scale-dependent limits come from combining CMB, BAO, and high-resolution Lyman-\(\alpha\) data. In the ETHOS parameterization, robust \(95\%\) limits are
\[
\Delta N_{\rm eff}<0.23,\qquad a_{\rm dark}\xi^4<30~{\rm Mpc}^{-1}
\]
for \(n=4\),
\[
\Delta N_{\rm eff}<0.29,\qquad 10^2 a_{\rm dark}\xi^4<18~{\rm Mpc}^{-1}
\]
for \(n=2\), and
\[
\Delta N_{\rm fluid}<0.47,\qquad 10^4 a_{\rm dark}\xi^4<14~{\rm Mpc}^{-1}
\]
for \(n=0\), with the caveat that for \(n=0\) the effective-rate bound is largely CMB-driven and the Lyman-\(\alpha\) applicability is more limited [1907.01496]. These bounds still leave room, especially for \(n=4\), for a cutoff in the halo mass function relevant to the missing-satellite problem.

The most aggressive Hubble-tension alleviation presently occurs in models with a small interacting DM fraction and decoupling near equality. Without ACT DR6 data, all three benchmark decoupling histories studied in that framework reduce the Hubble tension relative to \(\Lambda\)CDM, with the abrupt \(n=0\) case performing best; with SH0ES included, that case reaches
\[
H_0 = 72.6\,(72.6^{+1.6}_{-1.6})~{\rm km/s/Mpc},
\]
\[
\Delta N_{\rm eff}=0.89\,(0.86^{+0.31}_{-0.30}),
\]
\[
f_{\rm idm}=2.9\,(3.3^{+2.2}_{-2.2})\%,
\]
and \(\log_{10}z_{\rm dec}=3.3\,(3.3^{+0.1}_{-0.1})\). Once ACT DR6 is added, however, the fit is significantly worsened, and the largest \(H_0\) value at \(95\%\) confidence drops to \(70.1\) km/s/Mpc without SH0ES and rises only to \(72.5\) km/s/Mpc with SH0ES [2511.16554].

A complementary effective analysis that infers DAO from Planck plus SH0ES-calibrated supernovae finds
\[
H_0=72.40\pm0.91~\mathrm{km/s/Mpc},
\]
\[
\Delta N_{\rm eff}=0.85\pm0.17,
\]
\[
f_{\rm idm}=0.035^{+0.015}_{-0.013},
\]
\[
\log_{10}(z_{\rm dec})=3.316^{+0.075}_{-0.024},
\]
and a residual Hubble tension of \(2.3\sigma\), while simultaneously predicting a DAO feature at \(r_{d,\mathrm{DAO}}\sim 60~\mathrm{Mpc}/h\) with few-percent amplitude [2602.23895].

## 6. Boundaries of the concept and related scenarios

A recurrent misconception is that every DRMD paper computes a literal DM–DR scattering-decoupling epoch. Several influential works do not. Light thermal relics with \(M\le 20\) MeV that freeze out after neutrino decoupling modify \(T_\nu/T_\gamma\) and hence \(N_{\rm eff}\), but the relevant event is chemical freeze-out plus entropy transfer between already separated radiation baths. In that case, the non-equilibrium treatment strengthens both the increase of \(N_{\rm eff}\) for neutrino heating and the decrease of \(N_{\rm eff}\) for electromagnetic heating relative to the equilibrium approximation [1504.00773].

Likewise, the long-lived-decay scenario \(\chi_2\to\chi_1+f+\bar f\) realizes DRMD only in a kinematic sense. If
\[
\frac{M_1}{M_2}\ll 10^{-6}\sqrt{\frac{\tau}{\rm sec}},
\]
the daughter \(\chi_1\) stays relativistic to recombination and contributes to \(\Delta N_{\rm eff}\). If instead
\[
\frac{M_1}{M_2}\gtrsim 10^{-2}\sqrt{\frac{\tau}{10~{\rm sec}}},
\]
the daughter becomes non-relativistic early enough to be viable warm dark matter. The warm-DM branch predicts only
\[
\Delta N_{\rm eff}\lesssim 0.001,
\]
so the model yields either observable dark radiation or warm dark matter, but not both simultaneously at a significant level [1303.6267].

The background expansion history can also alter any DRMD sector without changing its microphysics. Freeze-out during an early matter-dominated era changes the Hubble scaling from \(H\propto T^2\) to \(H\propto T^{3/2}\), and late decay of the matter-dominating species dilutes the relic according to
\[
Y_{\rm relic}=\zeta\,Y_{\rm FO}.
\]
This is directly relevant whenever a DRMD sector is embedded in a nonstandard pre-BBN background, because the decoupling or freeze-out calculation then depends on the bath temperature relevant to the dark sector rather than on the visible temperature alone [1710.03758].

Finally, a systematic analysis of interacting dark radiation alone shows that present CMB+BAO data do not yet impose statistically significant constraints on the DR couplings once one allows free-streaming, fluid, decoupling, instantaneous decoupling, and recoupling cases in a unified relaxation-time framework. There is, however, a slight preference for the fluid-like limit, and in the instantaneous-decoupling case that limit corresponds to a late transition redshift around recombination [2212.13264]. This result isolates an important limiting case of DRMD: even without explicit DM drag, a transition between fluid-like and free-streaming radiation can already leave observable, and still currently allowed, signatures in the perturbation sector.

In that broader sense, DRMD is best understood not as a single model but as a structured class of dark-sector histories. Its central variables are the drag or transfer rate, the dark-radiation abundance, the fraction of dark matter participating in the interaction, the sharpness and timing of decoupling or conversion, and the thermodynamic relation between visible and dark sectors. The distinguishing empirical consequences are a time-dependent \(N_{\rm eff}\)-like radiation density, altered CMB acoustic structure, suppression or oscillation of the matter power spectrum, modified small-scale cutoff masses, and, in the most optimistic realizations, partial relief of the \(H_0\) and \(S_8\) tensions [1907.01496] [2511.16554] [2602.23895].

Source: https://www.emergentmind.com/topics/dark-radiation-matter-decoupling-drmd