The observational fact that the present values of the densities of dark energy and dark matter are of the same order of magnitude, ρ de0 /ρ dm0 ∼ O(1), seems to indicate that we are currently living in a very special period of the cosmic history. Within the standard model, a density ratio of the order of one just at the present epoch can be seen as coincidental since it requires very special initial conditions in the early Universe. The corresponding "why now" question constitutes the cosmological "coincidence problem". According to the standard model the equality ρ de = ρ dm took place "recently" at a redshift z ≈ 0.55. The meaning of "recently" is, however, parameter dependent. In terms of the cosmic time the situation looks different. We discuss several aspects of the "coincidence problem", also in its relation to the cosmological constant problem, to issues of structure formation and to cosmic age considerations.

By using observations of the Hulse-Taylor pulsar we constrain the gravitational wave (GW) speed to the level of 10 −2 . We apply this result to scalar-tensor theories that generalize Galileon 4 and 5 models, which display anomalous propagation speed and coupling to matter for GWs. We argue that this effect survives conventional screening due to the persistence of a scalar field gradient inside virialized overdensities, which effectively "pierces" the Vainshtein screening. In specific branches of solutions, our result allows to directly constrain the cosmological couplings in the effective field theory of dark energy formalism.

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 non-conservation 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-GR behaviour of the Rastall theory which should be 1% level. This work presents the more stringent constraints on the deviations of GR caused by the Rastall proposal.

Fluids often display dissipative properties. We explore dissipation in the form of bulk viscosity in the cold dark matter fluid. We constrain this model using current data from supernovae, baryon acoustic oscillations and the cosmic microwave background. Considering the isotropic and homogeneous background only, viscous dark matter is allowed to have a bulk viscosity 10 7 Pa·s, also consistent with the expected integrated Sachs-Wolfe effect (which plagues some models with bulk viscosity). We further investigate the small-scale formation of viscous dark matter halos, which turns out to place significantly stronger constraints on the dark matter viscosity. The existence of dwarf galaxies is guaranteed only for much smaller values of the dark matter viscosity, 10 −3 Pa·s. PACS numbers: 98.80-k, 95.36+x