Constraining dark matter properties with Cosmic Microwave Background observations

We examine how the properties of dark matter, parameterised by an equation of state parameter $w$ and two perturbative Generalised Dark Matter (GDM) parameters $c^2_s$ (the sound speed) and $c^2_\text{vis}$ (the viscosity), are constrained by existing cosmological data, particularly the Planck 2015 data release. We find that the GDM parameters are consistent with zero, and are strongly constrained, showing no evidence for extending the dark matter model beyond the Cold Dark Matter (CDM) paradigm. The dark matter equation of state is constrained to be within $-0.000896<w<0.00238$ at the $99.7\%$ confidence level, which is several times stronger than constraints found previously using WMAP data. The parameters $c^2_s$ and $c^2_\text{vis}$ are constrained to be less than $3.21\times10^{-6}$ and $6.06\times10^{-6}$ respectively at the $99.7\%$ confidence level. The inclusion of the GDM parameters does significantly affect the error bars on several $\Lambda$CDM parameters, notably the dimensionless dark matter density $\omega_g$ and the derived parameters $\sigma_8$ and $H_0$. This can be partially alleviated with the inclusion of data constraining the expansion history of the universe.