We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations. In order to compute the rate of formation of massive objects we employ the spherical collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press–Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift (number counts).

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We discuss the intriguing possibility that dark energy may change its equation of state in situations where large dark energy fluctuations are present. We show indications of this dynamical mutation in some generic models of dark energy.

There is a plethora of dark energy parameterizations that can fit current supernovae Ia data. However, this data is only sensitive to redshifts up to order one. In fact, many of these parameterizations break down at higher redshifts. In this paper we study the effect of dark energy models on the formation of dark halos. We select a couple of dark energy parameterizations which are sensible at high redshifts and compute their effect on the evolution of density perturbations in the linear and non-linear regimes. Using the Press-Schechter formalism we show that they produce distinguishable signatures in the number counts of dark halos. Therefore, future observations of galaxy clusters can provide complementary constraints on the behavior of dark energy.

ABSTRACT Although the search for extrasolar co-orbital bodies has not had success so far, it is believed that they must be as common as they are in the Solar system. Co-orbital systems have been widely studied, and there are several works on stability and even on formation. However, for the size and location of the stable regions, authors usually describe their results but do not provide a way to find them without numerical simulations, and, in most cases, the mass ratio value range is small. In this work, we study the structure of co-orbital stable regions for a wide range of mass ratio systems and build empirical equations to describe them. It allows estimating the size and location of co-orbital stable regions from a few system parameters. Thousands of massless particles were distributed in the co-orbital region of a massive secondary body and numerically simulated for a wide range of mass ratios (μ) adopting the planar circular restricted three-body problem. The results show that the upper limit of horseshoe regions is between 9.539 × 10−4 < μ < 1.192 × 10−3, which corresponds to a minimum angular distance from the secondary body to the separatrix of between 27.239º and 27.802º. We also found that the limit to existence of stability in the co-orbital region is about μ = 2.3313 × 10−2, much smaller than the value predicted by the linear theory. Polynomial functions to describe the stable region parameters were found, and they represent estimates of the angular and radial widths of the co-orbital stable regions for any system with 9.547 × 10−5 ≤ μ ≤ 2.331 × 10−2.