Dark Acoustic Oscillations (DAOs)

• Dark acoustic oscillations are oscillatory features arising from early-Universe interactions between a fraction of dark matter and dark radiation, establishing a distinct sound horizon in the power spectrum.
• DAO modeling employs a phenomenological transfer function with oscillatory and damping terms to capture small-scale suppression and multiple peaks in the linear matter power spectrum.
• Observational probes such as high-redshift UV luminosity functions, Lyman-α forest statistics, and 21-cm cosmology constrain DAO characteristics, guiding dark-sector model building.

Dark acoustic oscillations (DAOs) are oscillatory features imprinted on the cosmological matter power spectrum by early-Universe interactions between a fraction of dark matter (DM) and a relativistic “dark radiation” (DR) species. Analogous to baryon acoustic oscillations (BAOs) in the photon–baryon plasma, DAOs reflect pressure-driven sound waves in the coupled DM–DR fluid before kinetic decoupling. These oscillations introduce a characteristic scale—the dark-sector sound horizon—along with a series of damped features and small-scale suppression in the linear power spectrum. DAOs provide sensitive probes of dark-sector microphysics and are constrained observationally through effects on galaxy abundances, the cosmic microwave background (CMB), Lyman-α forest flux statistics, and 21-cm cosmology. This article surveys the physical origin of DAOs, formalism for their modeling, key observables, constraints from current data, and implications for dark-sector model building.

1. Physical Origin and Theoretical Framework

In a generic class of dark-sector models, a subcomponent of DM carries interactions—often through a light or massless mediator—that tightly couple it to a relativistic species, the DR, during the pre-decoupling epoch. Examples include atomic dark matter (aDM), DM–neutrino or DM–baryon scattering scenarios, and more generally, models captured by the ETHOS paradigm (Barron et al., 1 Dec 2025, Cyr-Racine et al., 2013, Bose et al., 2018, Muñoz et al., 2020, Buckley et al., 2014, Akita et al., 2023). While DM and DR remain coupled, pressure support from DR drives oscillatory behavior in the DM density perturbations. The relevant sound speed is

$c_{s,D}^2 = \frac{1}{3(1+R_D^{-1})},$

where $R_D = 3\rho_{\rm int}/4\rho_{\rm DR}$ is the DM-to-DR energy density ratio. This coupled fluid undergoes acoustic oscillations until the DM–DR momentum-exchange rate falls below the Hubble expansion, at the “drag” epoch $z_{\rm drag}$. Post-decoupling, the oscillatory structure is frozen in.

The comoving DAO sound horizon is

$$r_{\rm DAO} = \int_{z_{\rm drag}}^{\infty} \frac{c_{s,D}}{H(z)}\,dz,$$

setting the fundamental spatial scale for DAO features. Collisional (Silk-like) diffusion erases fluctuations at scales smaller than the DR mean free path, imposing a Gaussian damping envelope on the oscillations (Barron et al., 1 Dec 2025, Buckley et al., 2014). The relative amplitude, frequency, and damping of DAO features depend on the interacting DM fraction $f$, the strength and temperature dependence of the DM–DR cross-section, and the DR temperature ratio $\xi \equiv T_D/T_{\rm CMB}$.

2. Impact on the Linear Matter Power Spectrum

The principal signatures of DAOs in the linear matter power spectrum $P(k)$ are:

• A suppression of power at wavenumbers corresponding to scales inside the sound horizon at decoupling ($k \gtrsim k_{\rm start}$), with strength proportional to the interacting fraction $f$.
• A sequence of oscillatory (“wiggle”) features, with spacing set by the sound horizon:

$k_{\rm peak} \simeq \frac{2\pi}{r_{\rm DAO}},$

and oscillation frequency typically parameterized as $\omega \simeq 2.083\pi$ (Barron et al., 1 Dec 2025).

• A Silk-damped tail at higher wavenumbers.

To model these generic effects without solving full Boltzmann equations, a phenomenological transfer function is introduced (Barron et al., 1 Dec 2025): $$T(k) = \sqrt{\frac{P(k)}{P_{\rm CDM}(k)}} = T_{\alpha\beta\gamma\delta}(k) + T_{\rm osc}(k),$$ where

$$T_{\alpha\beta\gamma\delta}(k) = f\bigl[1+(\alpha\,k)^{\beta}\bigr]^{\gamma} + (1-f)$$

encodes WDM-like suppression, and

$$T_{\rm osc}(k) = \Theta(k-k_{\rm start})\,\bigl[ fA\cos\bigl( \omega (k/k_{\rm peak} - 1) \bigr) \bigr]\,\exp\bigl[-(k/k_d)^2\bigr]$$

models DAOs, with $A$ the first-peak height and $k_d$ the damping scale.

Special limits (e.g., $f\to 0$ or $k_{\rm peak}\to \infty$) recover the standard CDM result. The key distinction from warm dark matter is the presence of multiple peaks with independently adjustable amplitude and position.

3. Observational Signatures and Probes

3.1 High-Redshift UV Luminosity Function (UVLF)

DAO-induced suppression and oscillations modulate the population of collapsed dark-matter halos, especially at small scales and high redshifts, which in turn alter the abundance and luminosity distribution of early galaxies. The standard workflow is:

• Compute the modified halo mass function (HMF) using the extended Press–Schechter (EPS) formalism with a smoothing window calibrated to N-body simulations with DAO-initialized power (Barron et al., 1 Dec 2025, Akita et al., 2023). The Sheth–Tormen first-crossing distribution is adopted:

$$f_{\rm ST}(\nu) = A\sqrt{\frac{2q\nu}{\pi}}\bigl(1+(q\nu)^{-p}\bigr)\,\exp(-q\nu/2),$$

with appropriate parameters.

• Map the HMF to the UVLF via halo–galaxy modeling (e.g., GALLUMI), using a double power-law form for the star-formation efficiency and including log-normal scatter and nuisance parameter marginalization.
• Fit the resulting UVLF to data from Hubble, JWST, Subaru, and CFHT, marginalizing over astrophysical and DAO parameters using an MCMC framework (Barron et al., 1 Dec 2025).

3.2 Lyman-α Forest and 21-cm Cosmology

Hydrodynamical simulations show that DAOs imprint time- and scale-dependent "bumps" in the Lyman-α flux power spectrum at $z \gtrsim 5$, distinguishing DAO models from WDM or IGM thermal cutoff scenarios (Bose et al., 2018).

During cosmic dawn, DAOs modify the timing and shape of 21-cm brightness temperature fluctuations. The suppression and recovery of small-scale structure in ETHOS-like models lead to delayed, broadened global absorption features and shifted power-spectrum peaks, allowing discrimination between DAO-dominated and WDM-like suppression (Muñoz et al., 2020).

3.3 Local Structure: Satellite Galaxies and Subhalos

DAO-induced suppression in the subhalo HMF leads to reduced satellite abundances in Milky Way–like hosts. Comparison to observed satellite counts yields sharp constraints on DM–radiation interaction strengths, especially for energy-dependent cross sections: $$\sigma_{DM-\nu,0} < 4\times 10^{-34}\,\mathrm{cm}^2\,(m_{DM}/\mathrm{GeV}),$$ with even more stringent bounds for cross-sections rising with neutrino energy (Akita et al., 2023).

4. Current Cosmological Constraints

Combining probes of the matter power spectrum on small scales leads to the following constraints:

• High-redshift UVLF measurements require $k_{\rm peak} \gtrsim 50\,h/\mathrm{Mpc}$ at 95% confidence for interacting fraction $f \gtrsim 0.07$. For $f < 0.07$, DAOs remain unconstrained unless their features fall within the observable $k$-window. Profile likelihoods strengthen the bound to $k_{\rm peak} > 66\,h/\mathrm{Mpc}$ for $f=1$ (Barron et al., 1 Dec 2025).
• Planck CMB anisotropy and lensing data set weaker bounds ($k_{\rm peak} \gtrsim 3\,h/\mathrm{Mpc}$ for $f = 1$), and are most sensitive for large interacting fractions (Cyr-Racine et al., 2013).
• Lyman-α forest data at $z>5$ push $k_{\rm peak} \gtrsim 136\,h/\mathrm{Mpc}$ in some ETHOS scenarios with $n=4$ energy dependence, but do not yet cover strong-DAO regimes (Barron et al., 1 Dec 2025, Bose et al., 2018, Akita et al., 2023).
• Satellite galaxy counts exclude significant DAOs at mass scales $\gtrsim 10^8\,M_\odot$ for canonical cross-section parameterizations, placing limits on DM–neutrino coupling that supersede many CMB and Lyman-α bounds (Akita et al., 2023).

The table below summarizes representative constraints:

Probe	$k_{\rm peak}$ lower bound ($h/\mathrm{Mpc}$)	Interacting Fraction $f$	Reference
UVLF ($z=3-9$)	$\gtrsim 50-66$	$f \gtrsim 0.07-1$	(Barron et al., 1 Dec 2025)
Planck CMB	$\gtrsim 3$	$f=1$	(Cyr-Racine et al., 2013)
Lyman-α	$\gtrsim 136$, ($n=4$ ETHOS)	Model-dependent	(Barron et al., 1 Dec 2025)
MW satellites	$k_{\rm damp} \gg 10$	Model-dependent	(Akita et al., 2023)

5. Distinguishing DAOs from Other Models

DAO phenomenology is distinguished from WDM and baryonic/thermal suppression mechanisms by:

• The presence of localized oscillatory excess ("DAO bump") in linear and flux power spectra at scales set by $r_{\rm DAO}$, absent in WDM or Jeans-smoothing.
• Nonmonotonic suppression and potential recovery of small-scale halo abundances, as opposed to the smooth exponential cutoff in WDM.
• Evolution with redshift: nonlinear structure formation damps DAO wiggles in the 3D power spectrum by $z\sim6$, but signatures persist in Lyman-α and in the 1D flux power at high $z$ (Bose et al., 2018).

21-cm cosmology during cosmic dawn further separates DAO from WDM suppression by the relative timing and width of global features and by the scale-dependent power spectrum evolution (Muñoz et al., 2020).

6. Model Building Implications and Future Directions

DAOs provide stringent tests of hidden-sector models with light mediators or DM–Standard Model scattering (Barron et al., 1 Dec 2025, Cyr-Racine et al., 2013, Buckley et al., 2014, Akita et al., 2023). Measurements of small-scale power (via UVLF, satellites, Lyman-α, and 21-cm) can:

• Bound the allowed fraction of interacting DM to a few percent for scenarios with strong DAOs at observable scales, severely restricting models such as Double-Disk DM or atomic DM with late kinetic decoupling (Cyr-Racine et al., 2013, Barron et al., 1 Dec 2025).
• Place upper limits on DM–radiation cross sections, excluding large regions of parameter space invoked to address small-scale structure anomalies via DAO-induced suppression.
• Recasting constraints in terms of velocity-dependent cross sections, bounds from UVLF and satellites improve over Planck-era results by orders of magnitude—for example, $$\sigma_0 \lesssim 10^{-33} \,\mathrm{cm}^2/\mathrm{GeV}$$ for $n=4$ scaling (Barron et al., 1 Dec 2025).

Anticipated advances from deeper JWST surveys, Rubin and Roman Space Telescopes, 21-cm arrays, and improved modeling of low-mass galaxy formation are expected to push DAO constraints to even smaller scales and lower interacting fractions. Subdominant interacting DM components ($f \ll 1$) and models with very small $k_{\rm peak}$ remain the least constrained and will require next-generation data and refined theoretical modeling for robust exclusion or detection.

7. Summary

DAOs constitute a robust signature of DM–DR interactions in the early Universe, encoding microphysical properties of the dark sector in cosmological observables. Current constraints from high-redshift UVLF, CMB, Lyman-α forest, and satellite galaxy counts together restrict both the scale and the strength of DAOs. The model-independent phenomenological transfer function framework enables systematic comparison to data, and future multi-wavelength surveys are poised to further close the parameter space for DAO models, advancing the search for new physics in the dark sector (Barron et al., 1 Dec 2025, Cyr-Racine et al., 2013, Bose et al., 2018, Muñoz et al., 2020, Buckley et al., 2014, Akita et al., 2023).