The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

In the framework of the spherical collapse model, we study the influence of shear and rotation terms for dark matter fluid in clustering dark energy models. We evaluate, for different equations of state, the effects of these terms on the linear overdensity threshold parameter, δ_c, and on the virial overdensity, Δ_V. The evaluation of their effects on δ_c allows us to infer the modifications occurring on the mass function. Due to ambiguities in the definition of the halo mass in the case of clustering dark energy, we consider two different situations: the first is the classical one where the mass is of the dark matter halo only, while the second one is given by the sum of the mass of dark matter and dark energy. As previously found, the spherical collapse model becomes mass dependent and the two additional terms oppose the collapse of the perturbations, especially on galactic scales, with respect to the spherical non-rotating model, while on cluster scales the effects of shear and rotation become negligible. The values for δ_c and Δ_V are higher than the standard spherical model. Regarding the effects of the additional non-linear terms on the mass function, we evaluate the number density of haloes. As expected, major differences appear at high masses and redshifts. In particular, quintessence (phantom) models predict more (less) objects with respect to the Λ colddarkmatter model, and the mass correction due to the contribution of the dark energy component has negligible effects on the overall number of structures.

Models of dynamical dark energy unavoidably possess fluctuations in the energy density and pressure of that new component. In this paper we estimate the impact of dark energy fluctuations on the number of galaxy clusters in the Universe using a generalization of the spherical collapse model and the Press-Schechter formalism. The observations we consider are several hypothetical Sunyaev-Zel'dovich and weak lensing (shear maps) cluster surveys, with limiting masses similar to ongoing (SPT, DES) as well as future (LSST, Euclid) surveys. Our statistical analysis is performed in a 7-dimensional cosmological parameter space using the Fisher matrix method. We find that, in some scenarios, the impact of these fluctuations is large enough that their effect could already be detected by existing instruments such as the South Pole Telescope, when priors from other standard cosmological probes are included. We also show how dark energy fluctuations can be a nuisance for constraining cosmological parameters with cluster counts, and point to a degeneracy between the parameter that describes dark energy pressure on small scales (the effective sound speed) and the parameters describing its equation of state.

The possibility of dark matter being a dissipative component represents an option for the standard view where cold dark matter (CDM) particles behave on large scales as an ideal fluid. By including a physical mechanism in the dark matter description like viscosity, we construct a more realistic model for the Universe. Also, the known small scale pathologies of the standard CDM model either disappear or become less severe. We study clustering properties of a $\mathrm{\Lambda }\mathrm{CDM}$-like model in which dark matter is described as a bulk viscous fluid. The linear power spectrum, the nonlinear spherical "top hat" collapse, and the mass functions are presented. We use the analysis with such structure formation tools in order to place an upper bound on the magnitude of the dark matter’s viscosity.