Coupled dark energy: towards a general description of the dynamics

Abstract

In dark energy models of scalar-field coupled to a barotropic perfect fluid, theexistence of cosmological scaling solutions restricts the Lagrangian of the fieldφ top = Xg(Xeλφ), where , λ is aconstant and g is an arbitrary function. We derive general evolution equations in an autonomous form forthis Lagrangian and investigate the stability of fixed points for several different darkenergy 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 couplingQ between dark energy and dark matter. These fixed points are always classically stable for aphantom field, implying that the universe is eventually dominated by the energy density ofa scalar field if a phantom is responsible for dark energy. When the equation of statewφ for thefield φ islarger than −1, we find that scaling solutions are stable if the scalar-field dominant solution is unstable, andvice versa. Therefore in this case the final attractor is either a scaling solution with constantΩφ satisfying0 < Ωφ < 1 or a scalar-fielddominant solution with Ωφ = 1.