Coupled dark energy: Towards a general description of the dynamics

In dark energy models of scalar-field coupled to a barotropic perfect fluid, the existence of cosmological scaling solutions restricts the Lagrangian of the field φ to p ≤ Xg(Xe^λφ), where , λ is a constant and g is an arbitrary function. We derive general evolution equations in an autonomous form for this Lagrangian and investigate the stability of fixed points for several different dark energy models: (i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and (iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed points (Ω _φ ≤ 1) with an accelerated expansion in all models irrespective of the presence of the coupling Q between dark energy and dark matter. These fixed points are always classically stable for a phantom field, implying that the universe is eventually dominated by the energy density of a scalar field if a phantom is responsible for dark energy. When the equation of state w_φ for the field φ is larger than -1, we find that scaling solutions are stable if the scalar-field dominant solution is unstable, and vice versa. Therefore in this case the final attractor is either a scaling solution with constant Ω_φ satisfying 0 < Ω_φ < 1 or a scalar-field dominant solution with Ω_φ ≤ 1.