Coupled dark energy: Towards a general description of the dynamics

Abstract

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(Xeλϕ), where X = −g ν ∂ ϕ∂νϕ/2, 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 (Ωϕ = 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 phantom is responsible for dark energy. When the equation of state wϕ 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 Ωϕ satisfying 0 < Ωϕ < 1 or a scalar-field dominant solution with Ωϕ = 1