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 X = −g µν ∂µϕ∂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.PACS numbers: 98.70.Vc

We study cosmological perturbations in generalized Einstein scenarios and show the equivalence of inflationary observables both in the Jordan frame and the Einstein frame. In particular the consistency relation relating the tensor-to-scalar ratio with the spectral index of tensor perturbations coincides with the one in Einstein gravity, which leads to the same likelihood results in terms of inflationary observables. We apply this formalism to nonminimally coupled chaotic inflationary scenarios with potential V = cφ p and place constraints on the strength of nonminimal couplings using a compilation of latest observational data. In the case of the quadratic potential (p = 2), the nonminimal coupling is constrained to be ξ > −7.0 × 10 −3 for negative ξ from the 1σ observational contour bound. Although the quartic potential (p = 4) is under a strong observational pressure for ξ = 0, this property is relaxed by taking into account negative nonminimal couplings. We find that inflationary observables are within the 1σ contour bound as long as ξ < −1.7 × 10 −3 . We also show that the p ≥ 6 cases are disfavoured even in the presence of nonminimal couplings.

We consider a dynamical system of phantom scalar field under exponential potential in background of loop quantum cosmology. In our analysis, there is neither stable node nor repeller unstable node but only two saddle points, hence no Big Rip singularity. Physical solutions always possess potential energy greater than magnitude of the negative kinetic energy. We found that the universe bounces after accelerating even in the domination of the phantom field. After bouncing, the universe finally enters oscillatory regime.Comment: 8 pages, 6 figures, Revtex 4, Figures and References added. Version accepted by Physical Review D1

We investigate the phase space of a quintessence theory governed by a generalised version of the DBI action, using a combination of numeric and analytic methods. The additional degrees of freedom lead to a vastly richer phase space structure, where the field covers the full equation of state parameter space; −1 ≤ ω ≤ 1. We find many non-trivial solution curves to the equations of motion which indicate that DBI quintessence is an interesting candidate for a viable k-essence model.