The Cosmic Coincidence Problem in the Brane World

The so called ‘cosmic coincidence’ problem seems to suggest a coupling between dark energy and dark matter. A possibility could be given by dark matter particles with masses depending exponentially on the scalar field associated to dark energy. If the latter also has an exponential potential, attractor solutions exist with constant ΩDM and ΩDE and negative effective equation of state. Due to the very low mass of the dark energy field, its coupling to baryons should be strongly suppressed. Here we present a natural realization of this scenario in a model with large extra dimensions. 1 Coincidence Problem vs Equation of State One of the most puzzling aspects of the current cosmological paradigm, is the so-called ‘cosmic coincidence problem’, i.e. the quasi equivalence between dark matter (DM) and dark energy (DE) densities today. Indeed, for a noninteracting fluid A, the continuity equation d(ρAa ) = −pAda , relates the equation of state wA ≡ pA/ρA to the evolution of the energy density with the expansion, i.e., ρA ∼ a A. Therefore, the ratio between dark matter (wDM = 0) and a dark-energy component with negative pressure (wDE < 0) scales as ρDM ρDE ∼ aDE , (1) and could be only ‘coincidentally’ of order one today. This is the case for the cosmological constant (wDE = −1), for a scalar field with an inverse power law potential V (φ) ∼ φ (wDE = −2/(n+ 2)), or with any potential allowing solutions with negative pressure. On the other hand, exponential potentials exhibit attractor solutions in which there is no cosmic coincidence problem, since the scalar field energy density scales at a constant ratio with the background, be it matter or radiation. But, by virtue of eq. (1) this implies wDE = 0 after equivalence, thus making it unacceptable as a DE component. Thus, there seems to be an inextricable contradiction between a negative equation of state and the elimination of the cosmic coincidence. The impasse may be escaped by relaxing the assumption leading to eq. (1), i.e. by allowing an interaction between DM and DE, besides the gravitational one.