We study the fate of density perturbations in a Universe dominate by the Chaplygin gas, which exhibit negative pressure. In opposition to other models of perfect fluid with negative pressure, there is

Rastall's theory is based on the nonconservation of the energy-momentum tensor. We show that, in this theory, if we introduce a two-fluid model, one component representing vacuum energy whereas the other pressureless matter (e.g. baryons plus cold dark matter), the cosmological scenario is the same as for the $\Lambda${}CDM model, both at background and linear perturbation levels, except for one aspect: now dark energy may cluster. We speculate that this can lead to a possibility of distinguishing the models at the nonlinear perturbation level.

We calculate static and spherically symmetric solutions for the Rastall modification of gravity to describe neutron stars (NS). The key feature of the Rastall gravity is the nonconservation of the energy-momentum tensor proportionally to the space-time curvature. Using realistic equations of state for the NS interior we place a conservative bound on the non-general relativity behavior of the Rastall theory which should be $\lesssim 1\%$ level. This work presents the more stringent constraints on the deviations of general relativity caused by the Rastall proposal.

We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyze the corresponding Penrose diagrams revealing, in some cases, new causal structures.

We propose a scenario in which the dark components of the Universe are manifestations of a single bulk viscous fluid. Using dynamical system methods, a qualitative study of the homogeneous, isotropic background scenario is performed in order to determine the phase space of all possible solutions. The specific model which we investigate shares similarities with a generalized Chaplygin gas in the background but is characterized by nonadiabatic pressure perturbations. This model is tested against supernova type Ia and matter power spectrum data. Different from other unified descriptions of dark matter and dark energy, the matter power spectrum is well behaved, i.e., there are no instabilities or oscillations on small perturbation scales. The model is competitive in comparison with the currently most popular proposals for the description of the cosmological dark sector.

Different holographic dark-energy models are studied from a unifying point of view. We compare models for which the Hubble scale, the future event horizon or a quantity proportional to the Ricci scale are taken as the infrared cutoff length. We demonstrate that the mere definition of the holographic dark-energy density generally implies an interaction with the dark-matter component. We discuss the relation between the equation-of-state parameter and the energy density ratio of both components for each of the choices, as well as the possibility of noninteracting and scaling solutions. Parameter estimations for all three cutoff options are performed with the help of a Bayesian statistical analysis, using data from supernovae type Ia and the history of the Hubble parameter. The $\Lambda${}CDM model is the clear winner of the analysis. According to the Bayesian information criterion (BIC), all holographic models should be considered as ruled out, since the difference $\Delta${}BIC to the corresponding $\Lambda${}CDM value is >10. According to the Akaike information criterion (AIC), however, we find $\Delta${}AIC<2 for models with Hubble-scale and Ricci-scale cutoffs, indicating, that they may still be competitive. As we show for the example of the Ricci-scale case, also the use of certain priors, reducing the number of free parameters to that of the $\Lambda${}CDM model, may result in a competitive holographic model.