Structure Formation with Generalized Dark Matter

TL;DR

This work introduces generalized dark matter (GDM), a phenomenological framework that encodes dark matter gravitation through a stress-energy tensor parameterized by $w_g$, $c_{ m eff}^2$, and $c_{ m vis}^2$. By linking clustering properties to internal stresses rather than solely the background equation of state, the authors show how GDM can reproduce known candidates (CDM, HDM, radiation, scalar fields) while enabling distinct signatures in the matter power spectrum and CMB via a clustering scale $s_{ m eff}$ and a viscous scale $s_{ m vis}$. The analysis demonstrates that the clustering behavior can dramatically affect large-scale structure without equally altering CMB anisotropies, and vice versa, highlighting a path to constrain dark matter nature with upcoming observations. The paper also provides a bridge to scalar-field models and discusses time-dependent stresses (e.g., MDM) and single-component GDM scenarios, illustrating broad observational implications. Overall, the GDM framework offers a versatile toolkit to interpret future data and discriminate among dark matter candidates.

Abstract

The next generation of cosmic microwave background (CMB) experiments, galaxy surveys, and high-redshift observations can potentially determine the nature of the dark matter observationally. With this in mind, we introduce a phenomenological model for a generalized dark matter (GDM) component and discuss its effect on large-scale structure and CMB anisotropies. Specifying the gravitational influence of the otherwise non-interacting GDM requires not merely a model for its equation of state but one for its full stress tensor. From consideration of symmetries, conservation laws, and gauge invariance, we construct a simple but powerful 3 component parameterization of these stresses that exposes the new phenomena produced by GDM. Limiting cases include: a particle component (e.g. WIMPS, radiation or massive neutrinos), a cosmological constant, and a scalar field component. Intermediate cases illustrate how the clustering properties of the dark matter can be specified independently of its equation of state. This freedom allows one to alter the amplitude and features in the matter power spectrum relative to those of the CMB anisotropies while leaving the background cosmology fixed. Conversely, observational constraints on such properties can help determine the nature of the dark matter.

Figures (10)

• Figure 1: Large scale perturbation evolution ($k s_{\rm eff} \gg 1$) with GDM of $w_{g} = -1/6$, $c_{\rm eff}^2 = 1$ (solid, scalar fields) and $0$ (dashed, stress-gradient free). The Newtonian curvature $\Phi$ is independent of $c_{\rm eff}^2$ and varies only when the background equation of state changes at $a_{\rm eq}$ and $a_{g}$. However, the ratio of density perturbations in the GDM and matter depends on $c_{\rm eff}^2$. The cosmological parameters here are $\Omega_{\rm tot}=1$, $\Omega_{g}=0.9$, $\Omega_b h^2=0.0125$, $h=0.7$.
• Figure 2: Small-scale perturbation evolution for the GDM and the matter density perturbations in the same models as Fig. \ref{['fig:large']} with $c_{\rm eff}^2=1$ (dashed lines) and $c_{\rm eff}^2=0$ (solid lines). GDM perturbations stabilize once $k s_{\rm eff} > \pi$ and their relative absence ($\delta_g^{(\rm rest)}/\delta_m^{(\rm rest)} \ll 1$) then slow the growth of matter perturbations once the expansion is also GDM dominated $a>a_g$ leaving the potential $\Phi$ to decay.
• Figure 3: Viscous effects with GDM $w_{g}=1/3$ replacing the three species of massless neutrinos in the sCDM model ($\Omega_{\rm tot}=1 \approx \Omega_m$, $h=0.5$, $\Omega_b h^2=0.0125$). With the viscosity parameter set to mimic radiation $c_{\rm vis}^2=1/3$ (solid lines) the perturbations in the GDM decay whereas with $c_{\rm vis}^2=0$, they do not. This distinction has a negligible effect on the behavior of the potentials $\Phi$ and $\Psi$ well after sound horizon crossing
• Figure 4: The effective sound horizon and the COBE normalized matter power spectrum. Raising $c_{\rm eff}^2$ from 0 to 1 (solid lines) introduces a feature between the effective sound horizon at GDM-domination and that scale today. Here $\sigma_8=(0.75,0.29,0.25)$ and $\sigma_{50}/\sigma_8=(0.16,0.17,0.16)$ for $c_{\rm eff}^2=(0,1/6,1)$. These models have $w_{g}=-1/6$, $c_{\rm vis}^2=0$, $\Omega_{\rm tot}=1$, $\Omega_{g}=0.65$, $\Omega_b h^2=0.0125$, $h=0.7$ and tilt $n=1$. For comparison, the corresponding $\Lambda$-model ($w_{g} \rightarrow -1$, same parameters, $\sigma_8=1.1$, $\sigma_{50}/\sigma_8=0.16$, dashed lines), which fits the current large scale structure data, is also shown.
• Figure 5: (a) Modeling radiation. Shown here is the power spectrum for the model of Fig. \ref{['fig:timepi']} where GDM of $w_{g}=1/3$ replaces the neutrinos of sCDM. Altering the viscosity parameter from $c_{\rm vis}^2=1/3$ to $0$ has little effect on the power spectrum although $1/3$ is a somewhat better approximation at large scales. (b) Modeling HDM. The features of the mixed dark matter are well-reproduced by GDM with the same equation of state and $c_{\rm vis}^2=w_{g}$. The parameters here are sCDM with $\Omega_\nu=0.2$ replacing part of the CDM.