$\Lambda\alpha$DM: Observational constraints on unified dark matter with constant speed of sound

Abstract

We consider the hypothesis that dark energy and dark matter are the two faces of a single dark component, a unified dark matter (UDM) that we assume can be modeled by the affine equation of state (EoS) $P= p_0 +\alpha \rho$, resulting in an {\it effective cosmological constant} $\rho_\Lambda=-p_0/(1+\alpha)$. The affine EoS arises from the simple assumption that the speed of sound is constant; it may be seen as an approximation to an unknown barotropic EoS $P=P(\rho)$, and may as well represent the tracking solution for the dynamics of a scalar field with appropriate potential. Furthermore, in principle the affine EoS allows the UDM to be phantom. We constrain the parameters of the model, $\alpha$ and $\Omega_\Lambda$, using data from a suite of different cosmological observations, and perform a comparison with the standard $\Lambda$CDM model, containing both cold dark matter and a cosmological constant. First considering a flat cosmology, we find that the UDM model with affine EoS fits the joint observations very well, better than $\Lambda$CDM, with best fit values $\alpha=0.01 \pm 0.02$ and $\Omega_\Lambda=0.70 \pm 0.04$ (95% confidence intervals). The standard model (best fit $\Omega_\Lambda=0.71\pm 0.04$), having one less parameter, is preferred by a Bayesian model comparison. However, the affine EoS is at least as good as the standard model if a flat curvature is not assumed as a prior for $\Lambda$CDM. For the latter, the best fit values are $\Omega_K=-0.02^{+0.01}_{-0.02} $ and $\Omega_\Lambda=0.71 \pm 0.04$, i.e. a closed model is preferred. A phantom UDM with affine EoS is ruled out well beyond $3\sigma$.