Coupled dark energy: towards a general description of the dynamics

Abstract

In dark energy models of scalar-field coupled to a barotropic perfect fluid,\nthe existence of cosmological scaling solutions restricts the Lagrangian of the\nfield $\\vp$ to $p=X g(Xe^{\\lambda \\vp})$, where $X=-g^{\\mu\\nu} \\partial_\\mu \\vp\n\\partial_\\nu \\vp /2$, $\\lambda$ is a constant and $g$ is an arbitrary function.\nWe derive general evolution equations in an autonomous form for this Lagrangian\nand investigate the stability of fixed points for several different dark energy\nmodels--(i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and\n(iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed\npoints ($\\Omega_\\vp=1$) with an accelerated expansion in all models\nirrespective of the presence of the coupling $Q$ between dark energy and dark\nmatter. These fixed points are always classically stable for a phantom field,\nimplying that the universe is eventually dominated by the energy density of a\nscalar field if phantom is responsible for dark energy. When the equation of\nstate $w_\\vp$ for the field $\\vp$ is larger than -1, we find that scaling\nsolutions are stable if the scalar-field dominant solution is unstable, and\nvice versa. Therefore in this case the final attractor is either a scaling\nsolution with constant $\\Omega_\\vp$ satisfying $0<\\Omega_\\vp<1$ or a\nscalar-field dominant solution with $\\Omega_\\vp=1$.\n