---
title: Dark Acoustic Oscillations (DAOs)
url: https://www.emergentmind.com/topics/dark-acoustic-oscillations-daos
type: topic
---

# Dark Acoustic Oscillations (DAOs)

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 [2512.01998, 1310.3278, 1811.10630, 2011.05333, 1405.2075, 2305.01913]. 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 [2512.01998, 1405.2075]. 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 \( \omega \simeq 2.083\pi \) [2512.01998].

- A Silk-damped tail at higher wavenumbers.

To model these generic effects without solving full Boltzmann equations, a phenomenological transfer function is introduced [2512.01998]:
\[
T(k) = \sqrt{\frac{P(k)}{P_{\rm CDM}(k)}} = T_{\alpha\beta\gamma\delta}(k) + T_{\rm osc}(k),
\]
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 [2512.01998, 2305.01913]. 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 [2512.01998].

### 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 [1811.10630].

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 [2011.05333].

### 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 [2305.01913].

## 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 \( f=1 \) [2512.01998].

- 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 [1310.3278].

- 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 [2512.01998, 1811.10630, 2305.01913].

- 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 [2305.01913].

The table below summarizes representative constraints:

| Probe         | \( k_{\rm peak} \) lower bound (\( h/\mathrm{Mpc} \)) | Interacting Fraction \( f \) | Reference     |
|---------------|-----------------------------------------------------|-----------------------------|---------------|
| UVLF (\( z=3-9 \))   | \( \gtrsim 50-66 \)                            | \( f \gtrsim 0.07-1 \)      | [2512.01998]  |
| Planck CMB   | \( \gtrsim 3 \)                                      | \( f=1 \)                   | [1310.3278]   |
| Lyman-α      | \( \gtrsim 136 \), (\( n=4 \) ETHOS)                 | Model-dependent             | [2512.01998]  |
| MW satellites| \( k_{\rm damp} \gg 10 \)                            | Model-dependent             | [2305.01913]  |

## 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 \( z \) [1811.10630].

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 [2011.05333].

## 6. Model Building Implications and Future Directions

DAOs provide stringent tests of hidden-sector models with light mediators or DM–Standard Model scattering [2512.01998, 1310.3278, 1405.2075, 2305.01913]. 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 [1310.3278, 2512.01998].
- 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 [2512.01998].

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 [2512.01998, 1310.3278, 1811.10630, 2011.05333, 1405.2075, 2305.01913].

Source: https://www.emergentmind.com/topics/dark-acoustic-oscillations-daos