Yang–Mills condensate dark energy coupled with matter and radiation

Abstract

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 ρy(t) is taken to represent the dark energy, which is coupled either with the matter ρm(t), or with both the matter and the radiation components ρr(t). The effective YM Lagrangian is completely determined by the quantum field theory up to 1-loop order with an energy scale ∼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 ρmi = ρri, for a wide range of initial conditions of ρyi = (10−10, 10−2)ρmi, 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 Ωy ≃ 0.7, Ωm ≃ 0.3 and Ωr ≃ 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 wy = ρy/py crosses over −1 and takes the value wy ≃ −1.1 at z = 0. If the matter and radiation decay into the YMC, then ρm(t) ∝ a(t)−3 and ρr(t) ∝ 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 → ∞, the coupled dynamics for (ρy(t), ρm(t), ρr(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 ≃ (0.3–0.5) are inevitable. Thus the coincidence problem can be naturally solved in the YMC dark energy models.