While there is plentiful evidence in all fronts of experimental cosmology for the existence of a nonvanishing dark energy (DE) density ${\rho }_D$ in the Universe, we are still far away from having a fundamental understanding of its ultimate nature and of its current value, not even of the puzzling fact that ${\rho }_D$ is so close to the matter energy density ${\rho }_M$ at the present time (i.e. the so-called “cosmic coincidence” problem). The resolution of some of these cosmic conundrums suggests that the DE must have some (mild) dynamical behavior at the present time. In this paper, we examine some general properties of the simultaneous set of matter and DE perturbations $(\delta {\rho }_M,\delta {\rho }_D)$ for a multicomponent DE fluid. Next we put these properties to the test within the context of a nontrivial model of dynamical DE (the $\Lambda \mathrm{XCDM}$ model) which has been previously studied in the literature. By requiring that the coupled system of perturbation equations for $\delta {\rho }_M$ and $\delta {\rho }_D$ has a smooth solution throughout the entire cosmological evolution, that the matter power spectrum is consistent with the data on structure formation, and that the “coincidence ratio” $r={\rho }_D/{\rho }_M$ stays bounded and not unnaturally high, we are able to determine a well-defined region of the parameter space where the model can solve the cosmic coincidence problem in full compatibility with all known cosmological data.

• Received 6 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.043006