Partially Acoustic Dark Matter, Interacting Dark Radiation, and Large Scale Structure

TL;DR

The paper addresses discrepancies in H0 and σ8 within ΛCDM by proposing Partially Acoustic Dark Matter (PAcDM), where a subdominant DM component χ2 remains tightly coupled to a dark radiation fluid. This coupling induces dark acoustic oscillations that suppress χ2 perturbations and, in turn, the total DM growth on horizon-entry scales, while the DR component raises ΔNeff to help resolve the H0 tension. A concrete hidden WIMP realization provides a consistent thermal history for both DM components and DR, with χ2 comprising a few percent of the DM density and DR tuned to ΔNeff^scatt ≈ 0.25–0.4, yielding roughly 10% suppression in σ8 and small CMB deviations within current bounds. Numerical results show the mechanism is robust to DR fraction and hidden-sector parameters and make Stage-IV CMB/LSS tests viable, predicting measurable signatures in the matter power spectrum and lensing without forming a dark disk.

Abstract

The standard paradigm of collisionless cold dark matter is in tension with measurements on large scales. In particular, the best fit values of the Hubble rate $H_0$ and the matter density perturbation $σ_8$ inferred from the cosmic microwave background seem inconsistent with the results from direct measurements. We show that both problems can be solved in a framework in which dark matter consists of two distinct components, a dominant component and a subdominant component. The primary component is cold and collisionless. The secondary component is also cold, but interacts strongly with dark radiation, which itself forms a tightly coupled fluid. The growth of density perturbations in the subdominant component is inhibited by dark acoustic oscillations due to its coupling to the dark radiation, solving the $σ_8$ problem, while the presence of tightly coupled dark radiation ameliorates the $H_0$ problem. The subdominant component of dark matter and dark radiation continue to remain in thermal equilibrium until late times, inhibiting the formation of a dark disk. We present an example of a simple model that naturally realizes this scenario in which both constituents of dark matter are thermal WIMPs. Our scenario can be tested by future stage-IV experiments designed to probe the CMB and large scale structure.

Figures (2)

• Figure 1: Upper: Ratio of the DM power spectrum of the $r\neq 0$ case to the $r=0$ case, both with $\Delta N_\text{eff}^\text{scatt} = 0.4$. The curves are obtained by numerically solving the linear evolution equations (\ref{['eq:evolution:DM1']})--(\ref{['eq:evolution:DR']}) and the perturbed Einstein equation (\ref{['eq:evolution:psi']}), all in the tight coupling limit and assuming no anisotropic stress (hence $\sigma = 0$ and $\phi = \psi$). Results for different values of $r$ are labelled in different colors, while earlier ($a = 10^{-3}$) and later ($a=1$) times are indicated by dotted and solid lines, respectively. For the smaller scale structures $k \gtrsim 0.2h\>\mathrm{Mpc}^{-1}$, nonlinear gravitational effects become important so our linear approximation is no longer reliable. Lower: Same plot but with a reduced amount of DR, $\Delta N_\text{eff}^\text{scatt} = 0.05$.
• Figure 2: A comparison of the CMB spectrum between PAcDM and CDM models, assuming $\Delta N_\text{eff}^\text{scatt} =0.4$ in both cases. The black (red) curve is for the $\Lambda$CDM (PAcDM) model, derived from the $\{\delta_{\gamma},\theta_{\gamma}\}$ result in the linear evolution equations. The PAcDM model assumes the DM ratio $r=2.0\%$. For comparison, we also show a PAcDM model with $r=50\%$, which exhibits a clear enhancement of the expansion peaks and suppression of the compression peaks due to the pressure of tightly coupled DR.