Observationally Determining the Properties of Dark Matter

TL;DR

The paper develops a framework to observationally determine dark-sector properties using CMB, SN, and galaxy data within the generalized dark matter (GDM) parameterization, focusing on the background density $\Omega_g$, equation of state $w_g$, and perturbation properties $c_{ m eff}$ and $c_{ m vis}$. By leveraging the complementary redshift coverage and degeneracy-breaking power of each data set, the authors show that $w_g$ and $\Omega_g$ can be measured in a flat universe, and that $c_{ m eff}$ and $c_{ m vis}$ can be constrained to test quintessence versus other models. They demonstrate that, if the exotic component is not a cosmological constant, its clustering leaves measurable imprints on the CMB and galaxy power spectra; conversely, if it is a cosmological constant, the residual neutrino background radiation (NBR) can be probed through its anisotropies, potentially detectable with Planck. Overall, the work highlights the power of combining multi-wavelength cosmological probes to characterize dark matter properties and perform consistency checks across the standard cosmological model.

Abstract

Determining the properties of the dark components of the universe remains one of the outstanding challenges in cosmology. We explore how upcoming CMB anisotropy measurements, galaxy power spectrum data, and supernova (SN) distance measurements can observationally constrain their gravitational properties with minimal assumptions on the theoretical side. SN observations currently suggest the existence of dark matter with an exotic equation of state p/rho < -1/3 that accelerates the expansion of the universe. When combined with CMB anisotropy measurements, SN or galaxy survey data can in principle determine the equation of state and density of this component separately, regardless of their value, as long as the universe is spatially flat. Combining these pairs creates a sharp consistency check. If p/rho > -1/2, then the clustering behavior (sound speed) of the dark component can be determined so as to test the scalar-field ``quintessence'' hypothesis. If the exotic matter turns out instead to be simply a cosmological constant (p/rho = -1), the combination of CMB and galaxy survey data should provide a significant detection of the remaining dark matter, the neutrino background radiation (NBR). The gross effect of its density or temperature on the expansion rate is ill-constrained as it is can be mimicked by a change in the matter density. However, anisotropies of the NBR break this degeneracy and should be detectable by upcoming experiments.

Figures (10)

• Figure 1: Distance measure degeneracies: contours of constant (a) luminosity distance to $z=0.5$ ($H_0 d_L$) and (b) angular diameter distance to the last scattering surface ($H_0 d_A$). $\Omega_m h^2$ has been held fixed in the former under the assumption that the CMB acoustic peak morphology will measure it independently. With this assumption, the two distance measures provide complementary information.
• Figure 2: Current SN data. The 65%, 95% and 99% CL intervals in the $w_g-\Omega_g$ plane for the current data assuming only statistical errors. Constraints include 6 high redshift SN from the Supernova Cosmology Project Per97 and 10 from the High-z Supernova Search Gar97. We use 26 low-$z$ calibrating SN with $B-V<0.2$ obtained by the Calán/Tololo group CalTol. The analysis follows Whi98, but note that systematic errors may dominate in the current data sets.
• Figure 3: Sound speed effects for $w_g=-1/3$. A finite sound speed $c_{\rm eff}$ stabilizes perturbations leading to features in the (a) galaxy power spectrum and (b) CMB anisotropy spectrum. Note that in both cases the effects change most rapidly with $c_{\rm eff}$ between $0$ and $\sqrt{1/6}$. The power spectra have been normalized to small scales to bring out the degeneracies and the importance of large-scale information. The model here and throughout has $\Omega_m=0.35$, $h=0.65$, $\Omega_b h^2 = 0.02$, $\tau = 0.05$, $n=1$, and $T/S=0$.
• Figure 4: Viscosity effects: neutrinos may be accurately modeled as GDM with a viscosity parameter $c_{\rm vis}=\sqrt{1/3}$. Setting $c_{\rm vis}=0$ changes the CMB anisotropies significantly and equate to removing the quadrupole anisotropy of the NBR.
• Figure 5: Breaking the equation-of-state density degeneracy. The degeneracy exposed in Fig. \ref{['fig:distance']} can be broken by combining CMB information (here from MAP) with SN or galaxy survey (here from SDSS) information. Plotted here are the 68% CL for the various experiments and combinations. Comparison of the two combinations leads to a sharp consistency test. Two fiducial models are shown: (a) $w_g=-1/6$ and (b) $w_g=-1$. While the CMB alone does well at $w_g=-1/6$, its degeneracy worsens considerably as $w_g$ decreases toward $-1$. Note, however, that the complementary nature of the data sets and the ability to make consistency checks occurs in both cases.