The observational fact that the present values of the densities of dark energy and dark matter are of the same order of magnitude, $rho_{de0}/rho_{dm0} sim mathcal{O}(1)$, 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 $rho_{de} = rho_{dm}$ took place recently at a redshift $z approx 0.55$. 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.
Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static configurations.
General relativity solutions for stars are known as the Tolman-Oppenheimer-Volkoff (TOV) equations. On the other hand, the Newtonian description does not take into account the total pressure effects and therefore can not be used in strong field regimes. We discuss how to incorporate pressure in the stellar equilibrium equations within the neo-Newtonian framework. We compare the Newtonian, neo-Newtonian and the full relativistic theory by solving the equilibrium equations for both three approaches and calculating the mass-radius diagrams for some simple neutron stars equation of state.
We assume cold dark matter to possess a small bulk-viscous pressure which typically attenuates the growth of inhomogeneities. Explicit calculations, based on Eckarts theory of dissipative processes, reveal that for viscous cold dark matter the usual
Newtonian approximation for perturbation scales smaller than the Hubble scale is no longer valid. We advocate the use of a neo-Newtonian approach which consistently incorporates pressure effects into the fluid dynamics and correctly reproduces the general relativistic dynamics. This result is of interest for numerical simulations of nonlinear structure formation involving nonstandard dark-matter fluids. We obtain upper limits on the magnitude of the viscous pressure by requiring that relevant perturbation amplitudes should grow sufficiently to enter the nonlinear stage.
