Unified Dark Matter models with fast transition

We investigate the general properties of Unified Dark Matter (UDM) fluid models where the pressure and the energy density are linked by a barotropic equation of state (EoS) $p = p( ho)$ and the perturbations are adiabatic. The EoS is assumed to admit a future attractor that acts as an effective cosmological constant, while asymptotically in the past the pressure is negligible. UDM models of the dark sector are appealing because they evade the so-called "coincidence problem" and "predict" what can be interpreted as $w_{ m DE} approx -1$, but in general suffer the effects of a non-negligible Jeans scale that wreak havoc in the evolution of perturbations, causing a large Integrated Sachs-Wolfe effect and/or changing structure formation at small scales. Typically, observational constraints are violated, unless the parameters of the UDM model are tuned to make it indistinguishable from $Lambda$CDM. Here we show how this problem can be avoided, studying in detail the functional form of the Jeans scale in adiabatic UDM perturbations and introducing a class of models with a fast transition between an early Einstein-de Sitter CDM-like era and a later $Lambda$CDM-like phase. If the transition is fast enough, these models may exhibit satisfactory structure formation and CMB fluctuations. To consider a concrete case, we introduce a toy UDM model and show that it can predict CMB and matter power spectra that are in agreement with observations for a wide range of parameter values.