Interacting dark energy, holographic principle, and coincidence problem

The interacting and holographic dark energy models involve two important quantities. One is the characteristic size of the holographic bound and the other is the coupling term of the interaction between dark energy and dark matter. Rather than fixing either of them, we present a detailed study of theoretical relationships among these quantities and cosmological parameters as well as observational constraints in a general formalism. In particular, we argue that the ratio of dark matter to dark energy density depends on the choice of these two quantities, thus providing a mechanism to change the evolution history of the ratio from that in standard cosmology such that the coincidence problem may be solved. We investigate this problem in detail and construct explicit models to demonstrate that it may be alleviated provided that the interacting term and the characteristic size of holographic bound are appropriately specified. Furthermore, these models are well fitted with the current observation at least in the low redshift region.