Clustered unified dark sector cosmology: Background evolution and linear perturbations in light of observations

We consider unified dark sector models in which the fluid can collapse and cluster into halos, allowing for hierarchical structure formation to proceed as in standard cosmology. We show that both background evolution and linear perturbations tend towards those in $\LCDM$ as the clustered fraction $f \rightarrow 1$. We confront such models with various observational datasets, with emphasis on the relatively well motivated standard Chaplygin gas. We show that the strongest constraints come from secondary anisotropies in the CMB spectrum, which prefer models with $f \rightarrow 1$. However, as a larger Hubble constant is allowed for smaller $f$, values of $f \simeq 0.99$ (rather than tending to exact unity) are favored when late universe expansion data is included, with $f \simeq 0.97$ and $H_0 \simeq 70 {\rm km/s/Mpc}$ allowed at the 2-$\sigma$ level. Such values of $f$ imply extremely efficient clustering into nonlinear structures. They may nevertheless be compatible with clustered fractions in warm dark matter based cosmologies, which have similar minimal halo mass scales as the models considered here. Tight CMB constraints on $f$ also apply to the generalized Chaplygin gas, except for models that are already quite close to $\LCDM$, in which case all values of $0 \le f \le 1$ are allowed. In contrast to the CMB, large scale structure data, which were initially used to rule out unclustered unified dark matter models, are far less constraining. Indeed, late universe data, including the large scale galaxy distribution, prefer models that are far from $\LCDM$. But these are in tension with the CMB data.