Spherical collapse in quintessence models with zero speed of sound
  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.
