Spherical collapse of dark energy with an arbitrary sound speed
  We consider a generic type of dark energy fluid, characterised by a constant
equation of state parameter w and sound speed c_s, and investigate the impact
of dark energy clustering on cosmic structure formation using the spherical
collapse model. Along the way, we also discuss in detail the evolution of dark
energy perturbations in the linear regime. We find that the introduction of a
finite sound speed into the picture necessarily induces a scale-dependence in
the dark energy clustering, which in turn affects the dynamics of the spherical
collapse in a scale-dependent way. As with other, more conventional fluids, we
can define a Jeans scale for the dark energy clustering, and hence a Jeans mass
M_J for the dark matter which feels the effect of dark energy clustering via
gravitational interactions. For bound objects (halos) with masses M >> M_J, the
effect of dark energy clustering is maximal. For those with M << M_J, the dark
energy component is effectively homogeneous, and its role in the formation of
these structures is reduced to its effects on the Hubble expansion rate. To
compute quantitatively the virial density and the linearly extrapolated
threshold density, we use a quasi-linear approach which is expected to be valid
up to around the Jeans mass. We find an interesting dependence of these
quantities on the halo mass M, given some w and c_s. The dependence is the
strongest for masses lying in the vicinity of M ~ M_J. Observing this
M-dependence will be a tell-tale sign that dark energy is dynamic, and a great
leap towards pinning down its clustering properties.
