We study the spherical collapse model in the presence of quintessence with
negligible speed of sound. This case is particularly motivated for w<-1 as it
is required by stability. As pressure gradients are negligible, quintessence
follows dark matter during the collapse. The spherical overdensity behaves as a
separate closed FLRW universe, so that its evolution can be studied exactly. We
derive the critical overdensity for collapse and we use the extended
Press-Schechter theory to study how the clustering of quintessence affects the
dark matter mass function. The effect is dominated by the modification of the
linear dark matter growth function. A larger effect occurs on the total mass
function, which includes the quintessence overdensities. Indeed, here
quintessence constitutes a third component of virialized objects, together with
baryons 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 total
mass function at low redshift.Comment: 38 pages; small changes, including modification of the window
function. JCAP published versio
