Interacting Dark Matter disguised as Warm Dark Matter

TL;DR

The paper investigates Dark Matter–photon interactions and their imprint on cosmological perturbations, computing both CMB anisotropies and the matter power spectrum under an Interacting Dark Matter (IDM) framework. It identifies a novel weak-coupling damping regime that suppresses DM fluctuations as they enter the horizon, in addition to conventional Silk damping, and shows that IDM can masquerade as Warm Dark Matter in the small-scale power spectrum while leaving CMB signatures largely intact. A phenomenological transfer function for IDM, T_IDM(k), is derived and shown to map to a WDM-like suppression for appropriate cross sections, with alpha ~ 0.073 Mpc and nu = 1.2; this enables a direct comparison to WDM constraints. Using large-scale structure and Lyman-Alpha forest considerations, the authors derive a stringent bound on the cross section-to-mass ratio: $\sigma_{\gamma-DM}/m_{DM} \lesssim 10^{-32}\ \mathrm{cm^2\,GeV^{-1}}$, implying DM decouples before Silk damping yet can still produce notable small-scale power suppression. Overall, IDM constitutes a viable WDM-like scenario with distinct observational signatures and tight constraints on photon–Dark Matter interactions.

Abstract

We explore some of the consequences of Dark Matter-photon interactions on structure formation, focusing on the evolution of cosmological perturbations and performing both an analytical and a numerical study. We compute the cosmic microwave background anisotropies and matter power spectrum in this class of models. We find, as the main result, that when Dark Matter and photons are coupled, Dark Matter perturbations can experience a new damping regime in addition to the usual collisional Silk damping effect. Such Dark Matter particles (having quite large photon interactions) behave like Cold Dark Matter or Warm Dark Matter as far as the cosmic microwave background anisotropies or matter power spectrum are concerned, respectively. These Dark Matter-photon interactions leave specific imprints at sufficiently small scales on both of these two spectra, which may allow to put new constraints on the acceptable photon-Dark Matter interactions. Under the conservative assumption that the abundance of 10^12 M_sol galaxies is correctly given by Cold Dark Matter, and without any knowledge of the abundance of smaller objects, we obtain the limit on the ratio of the Dark Matter-photon cross section to the Dark Matter mass sigma_{gamma-DM} / m_DM < 10^-6 sigma_Thomson / 100 GeV \sim 6 * 10^-33 cm^2 GeV^-1 .

Figures (5)

• Figure 1: Evolution of Dark Matter density perturbation as a function of the redshift for various ( large) interaction rates with photons, all leading to collisional damping. In this plot, as in the others, we consider a Dark Matter model with a cosmological constant, with $h = 0.65$ (i.e., $H_0 = 100 h \,{\rm km}^{} \,{\rm s}^{-1} \,{\rm Mpc}^{-1}$), $\Omega_{\Lambda} = 0.7$, $\Omega_{\rm mat} = 0.3$, $\Omega_{\rm b} h^2 = 0.019$, and a scalar perturbation index $n_{\rm S} = 1$. We have considered the mode $k = 40 \,{\rm Mpc}^{- 1}$. At $z > 10^7$, the mode is outside the Hubble radius and the perturbation is frozen. The perturbation first experiences undamped oscillations (strong coupling regime) and then exponentially damped oscillations, corresponding to the collisional damping regime. The $\gamma - {\rm DM}$ cross sections are parameterized by the quantity $u \equiv [\sigma_ { \gamma - {\rm DM} } / \sigma_{\rm Th} ] [m_{\rm DM} / 100 \,{\rm GeV}^{} ]^{- 1}$.
• Figure 2: Evolution of CDM density perturbation as a function of the redshift for various (small) interaction rates with photons. As expected, for sufficiently small cross sections, almost no effect is noticeable. For slightly larger cross sections, the coupling between Dark Matter and photons stops just after the mode has entered into the Hubble radius, preventing the perturbation from experiencing the small growth in the radiation dominated era.
• Figure 3: Evolution of CDM density perturbation as a function of the redshift for various (intermediate) interaction rates with photons. As explained in the text, the Dark Matter perturbations experience a power law decay due to their weak coupling to photons. This is the main effect we can expect to have at small scales for acceptable cross sections.
• Figure 4: Influence of Interacting Dark Matter on the CMB anisotropy spectrum as a function of the Dark-Matter--photon cross section. The most spectacular effect which occurs at sufficiently large $\sigma_ { \gamma - {\rm DM} }$ is the apparent damping due to the large width of the last scattering surface, with some additional collisional damping due to photon--Dark-Matter interactions, and a slight shift of the Doppler peaks due to the decreases of the sound speed in the Dark-Matter--baryon--photon "plasma".
• Figure 5: Influence of Interacting Dark Matter on the matter power spectrum. As explained in the text, the deviation from a CDM power spectrum exhibits several regimes, the strong coupling regime, the collisional damping regime, and the neutrino regime. The cosmological parameters here are the same as for Fig. \ref{['fig_b4']}. The wiggles at very small scales for large cross section are due to some unimportant numerical accuracy problems.