The growth of fluctuations in Chaplygin gas cosmologies: A nonlinear Jeans scale for unified dark matter

Unified dark matter cosmologies economically combine missing matter and energy in a single fluid. Of these models, the standard Chaplygin gas is theoretically motivated, but faces problems in explaining large scale structure if linear perturbations are directly imposed on the homogeneous fluid. However, early formation of a clustered component of small halos is sufficient (and necessary) for hierarchical clustering to proceed in a CDM-like component as in the standard scenario, with the remaining homogeneous component acting as dark energy. We examine this possibility. A linear analysis shows that a critical Press-Schecter threshold for collapse can generally only be reached for generalized Chaplygin gas models that mimic $\Lambda$CDM, or ones where superluminal sound speeds occur. But the standard Chaplygin gas case turns out to be marginal, with overdensities reaching order one in the linear regime. This motivates a nonlinear analysis. A simple infall model suggests that collapse is indeed possible for perturbations of order 1~kpc and above; for, as opposed to standard gases, pressure forces decrease with increasing densities, allowing for the collapse of linearly stable systems. This suggests that a cosmological scenario based on the standard Chaplygin gas may not be ruled out from the viewpoint of structure formation, as often assumed. On the other hand, a 'nonlinear Jeans scale', constricting growth to scales $R \gtrsim {\rm kpc}$, which may be relevant to the small scale problems of CDM, is predicted. Finally, the background dynamics of clustered Chaplygin gas cosmologies is examined and confronted with observational datasets. It is found to be viable (at 1-sigma), with a mildly larger $H_0$ than $\Lambda$CDM, if the clustered fraction is larger than $90 \%$.