In this Letter we demonstrate that any interaction of pressureless dark matter with holographic dark energy, whose infrared cutoff is set by the Hubble scale, implies a constant ratio of the energy densities of both components thus solving the coincidence problem. The equation of state parameter is obtained as a function of the interaction strength. For a variable degree of saturation of the holographic bound the energy density ratio becomes time dependent which is compatible with a transition from decelerated to accelerated expansion.Comment: 9 pages, no figures, references updated, typos eliminated. To be published in Physics Letters

A model consisting of quintessence scalar field interacting with cold dark matter is considered. Conditions required to reach w d = −1 are discussed. It is shown that depending on the potential considered for the quintessence, reaching the phantom divide line puts some constraints on the interaction between dark energy and dark matter. This also may determine the ratio of dark matter to dark energy density at w d = −1. PACS: 98.80.-k, 95.36.+x

We show that a suitable interaction between a scalar field and a matter fluid in a spatially homogeneous and isotropic spacetime can drive the transition from a matter dominated era to an accelerated expansion phase and simultaneously solve the coincidence problem of our present Universe. For this purpose we study the evolution of the energy density ratio of these two components.We demonstrate that a stationary attractor solution is compatible with an accelerated expansion of the Universe. We extend this study to account for dissipation effects due to interactions in the dark matter fluid. Finally, Type Ia supernovae and primordial nucleosynthesis data are used to constrain the parameters of the model.

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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.