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We study the spherical collapse model in the presence of quintessence withnegligible speed of sound. This case is particularly motivated for w<-1 as itis required by stability. As pressure gradients are negligible, quintessencefollows dark matter during the collapse. The spherical overdensity behaves as aseparate closed FLRW universe, so that its evolution can be studied exactly. Wederive the critical overdensity for collapse and we use the extendedPress-Schechter theory to study how the clustering of quintessence affects thedark matter mass function. The effect is dominated by the modification of thelinear dark matter growth function. A larger effect occurs on the total massfunction, which includes the quintessence overdensities. Indeed, herequintessence constitutes a third component of virialized objects, together withbaryons and dark matter, and contributes to the total halo mass by a fraction ~(1+w) Omega_Q / Omega_m. This gives a distinctive modification of the totalmass function at low redshift.

Spherical collapse in quintessence models with zero speed of sound