Yang-Mills condensate dark energy coupled with matter and radiation

The coincidence problem is studied for the dark energy model of effective Yang-Mills condensate (YMC) in a flat expanding universe during the matter dominated stage. The YMC energy rho(y)(t) is taken to represent the dark energy, which is coupled either with the matter rho(m)(t), or with both the matter and the radiation components rho(r) (t). The effective YM Lagrangian is completely determined by the quantum field theory up to 1-loop order with an energy scale similar to 10(-3) eV as a model parameter, and for each coupling, there is an extra model parameter. We have studied extensively the coupling models: the YMC decaying into the matter and the radiation; or vice versa the matter and radiation decaying into the YMC. It is found that, starting from the equality of radiation-matter rho(mi) = rho(ri), for a wide range of initial conditions of rho(yi) = (10(-10), 10(-2))rho(mi), the models have a scaling solution during the early stages, and the YMC levels off and becomes dominant at late time, and the present state with Omega(y) similar or equal to 0.7, Omega(m) similar or equal to 0.3 and Omega(r) similar or equal to 10(-5) is always achieved. If the YMC decays into a component, then this component also levels off later and approaches a constant value asymptotically, and the equation of state (EoS) of the YMC w(y) = rho(y)/p(y) crosses over -1 and takes the value w(y) similar or equal to -1.1 at z = 0. If the matter and radiation decay into the YMC, then rho(m)(t) proportional to a(t)(-3) and rho(r) (t) proportional to a(t)(-4) approximately for all the time, and wy approaches -1 but does not cross over-1. We have also demonstrated that, at t -> infinity, the coupled dynamics for (rho(y) (t), rho(m)(t), rho(r) (t)) is a stable attractor. Therefore, under generic circumstances, the existence of the scaling solution during the early stages and the subsequential exit from the scaling regime around z similar or equal to ( 0.3-0.5) are inevitable. Thus the coincidence problem can be naturally solved in the YMC dark energy models.