Late-time Attractor Research Articles

Development of the Model of the Generalized Quintom DarkEnergy

We consider a generalized quintom (GQ) dark energy model for changingthe equal weight of the negative-kinetic scalar field (phantom) and thenormal scalar field (quintessence) in quintom dark energy. Though thephantom-dominated scaling solution is a stable late-time attractor, theearly evolution of GQ is different from that of the quintom model andthe adjustability of the dark energy state equation in the model isimproved.

THE EVOLUTION OF THE UNIVERSE WITH THE B–I TYPE PHANTOM SCALAR FIELD

We consider the phantom cosmology with a Lagrangian [Formula: see text] originated from the nonlinear Born–Infeld type scalar field. This cosmological model can explain the accelerating expansion of the universe with the equation of state parameter w ≤ -1. We get a sufficient condition for an arbitrary potential that admits a late time attractor solution: the value of potential u(Xc) at the critical point (Xc, 0) should be maximum and greater than zero. We study a specific potential with the form of [Formula: see text] via phase plane analysis and compute the cosmological evolution by numerical analysis in detail. The results show that the phantom field survives till today (to account for the present observed accelerating expansion) without interfering with the nucleosynthesis of the standard model (the density parameter Ωϕ≃10-12 at the equipartition epoch), and also avoid the future collapse of the universe.

Cosmic no hair for braneworlds with a bulk dilaton field

Braneworld cosmology supported by a bulk scalar field with an exponentialpotential is developed. A general class of separable backgrounds for bothsingle and two-brane systems is derived, where the bulk metric componentsare given by products of world volume and bulk coordinates and the world-volumesrepresent any anisotropic and inhomogeneous solution to an effective four-dimensionalBrans-Dicke theory of gravity. We deduce a cosmic no hair theorem for allever-expanding, spatially homogeneous Bianchi world volumes and find thatthe spatially flat and isotropic inflationary scaling solution representsa late-time attractor when the bulk potential is sufficiently flat. The dependenceof this result on the separable nature of the bulk metric is investigatedby applying the techniques of Hamilton-Jacobi theory to five-dimensional Einsteingravity. We employ the spatial gradient expansion method to determine theasymptotic form of the bulk metric up to third-order in spatial gradients.It is found that the condition for the separable form of the metric to representthe attractor of the system is precisely the same as that for the four-dimensionalworld-volume to isotropize. We also derive the fourth--order contributionto the Hamilton-Jacobi generating functional. Finally, we conclude by placingour results within the context of the holographic approach to braneworld cosmology.

INDUCED PHANTOM AND 5D ATTRACTOR SOLUTION IN SPACETIME–MATTER THEORY

In Spacetime–Matter theory we assume that the 4D induced matter of the 5D Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and phantom models of dark energy could be recovered from the 5D cosmological solutions. By using the phase-plane analysis to study the stability of evolution of the 5D models, we find that the conventional 4D late-time attractor solution is also recovered. This attractor solution shows that the scale factors of the phantom dominated universes in both the 4D and 5D theories will reach infinity in a finite time and the universes will be ended at a new kind of spacetime singularity at which everything will be annihilated. We also find that the repulsive force of the phantom may provide us with a mechanics to explain the bounce.

Cosmological constraints on a classical limit of quantum gravity

We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors - one accelerating and the other dramatically decelerating. It is also shown that nonaccelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements.

Inhomogeneous perturbations of plane-wave spacetimes

Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary γ-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalized scale-invariant variables, we show that these solutions are unstable to generic inhomogeneous perturbations. The crucial observation for establishing this result is a divergence of the expansion-normalized frame variables which ultimately leads to unstable modes.

Phantom cosmology with general potentials

We present a unified treatment of the phase space of a spatially flat homogeneous and isotropic universe dominated by a phantom field. Results on the dynamics and the late time attractors (big rip, de Sitter, etc) are derived without specifying the form of the phantom potential, using only general assumptions on its shape. Many results found in the literature are quickly recovered and predictions are made for new scenarios.

Asymptotic behavior of Cardassian cosmologies with exponential potentials

In this paper we analyze the asymptotic behavior of Cardassian cosmological models filled with a perfect fluid and a scalar field with an exponential potential. Cardassian cosmologies arise from modifications of the Friedmann equation, and among the different proposals within that framework we will choose those of the form $3H^2-\rho\propto \rho^n$ with $n<1$. We construct two three dimensional dynamical systems arising from the evolution equations, respectively adapted for studying the high and low energy limits. Using standard dynamical systems techniques we find the fixed points and characterize the solutions they represent. We pay especial attention to the properties inherent to the modifications and compare with the (standard) unmodified scenario. Among other interesting results, we find there are no late-time tracking attractors.

FIVE-DIMENSIONAL COSMOLOGICAL SCALING SOLUTION

A five-dimensional Ricci-flat cosmological solution is studied by assuming that the induced 4D matter contains two components: the usual fluid for dark matter as well as baryons and a scalar field with an exponential potential for dark energy. With use of the phase-plane analysis it is shown that there exist two late-time attractors one of which corresponds to a universe dominated by the scalar field alone and the other is a scaling solution in which the energy density of the scalar field remains proportional to that of the dark matter. It is furthermore shown that for this 5D scaling solution the universe expands with the same rate as in the 4D FRW models and not relies on which 4D hypersurface the universe is located in the 5D manifold.

Properties of singularities in the (phantom) dark energy universe

The properties of future singularities are investigated in the universe dominated by dark energy including the phantom-type fluid. We classify the finite-time singularities into four classes and explicitly present the models which give rise to these singularities by assuming the form of the equation of state of dark energy. We show the existence of a stable fixed point with an equation of state $w&lt;\ensuremath{-}1$ and numerically confirm that this is actually a late-time attractor in the phantom-dominated universe. We also construct a phantom dark energy scenario coupled to dark matter that reproduces singular behaviors of the Big Rip type for the energy density and the curvature of the universe. The effect of quantum corrections coming from conformal anomaly can be important when the curvature grows large, which typically moderates the finite-time singularities.

Cosmological evolution of a quintom model of dark energy

We investigate in this Letter the cosmological evolution of a dark energy model with two scalar fields where one of the scalar has canonical kinetic energy and another scalar has negative kinetic energy term. For such a system with exponential potentials we find that during the evolution of the universe the equation of state w changes from w⩾−1 to w<−1, which is consistent with the recent observations. A phase-plane analysis shows that the “phantom”-dominated scaling solution is the stable late-time attractor of this type of models.

The asymptotic behaviour of tilted Bianchi type VI0 universes

We study the asymptotic behaviour of the Bianchi type VI0 universes with a tilted γ-law perfect fluid. The late-time attractors are found for the full seven-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, γ = 6/5, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point and an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for γ < 2.

Cosmological scaling solutions and cross-coupling exponential potential

We present a phase-space analysis of cosmology containing multiple scalar fields with a positive or negative cross-coupling exponential potential. We show that there exist power-law kinetic–potential-scaling solutions for a sufficiently flat positive potential or for a steep negative potential. The former is the unique late-time attractor, but it is difficult to yield assisted inflation. The later is never stable in an expanding universe. Moreover, for a steep negative potential there exists a kinetic-dominated regime in which each solution is a late-time attractor. In the presence of ordinary matter these scaling solutions with a negative cross-coupling potential are found unstable. We briefly discuss the physical consequences of these results.

Phantom with Born-Infeld-type Lagrangian

Recent analysis of the observation data indicates that the equation of state of the dark energy might be smaller than -1, which leads to the introduction of phantom models featured by its negative kinetic energy to account for the regime of equation of state $w<-1$. In this paper, we generalize the idea to the Born-Infield type Lagrangian with negative kinetic energy term and give the condition for the potential, under which the late time attractor solution exists and also analyze a viable cosmological model in such a scheme.

Cosmological dynamics of a phantom field

We study the general features of the dynamics of the phantom field in the cosmological context. In the case of inverse coshyperbolic potential, we demonstrate that the phantom field can successfully drive the observed current accelerated expansion of the universe with the equation of state parameter $w_{\phi} < -1$. The de-Sitter universe turns out to be the late time attractor of the model. The main features of the dynamics are independent of the initial conditions and the parameters of the model. The model fits the supernova data very well, allowing for $-2.4 < w_{\phi} < -1$ at 95 % confidence level.

Cosmological scaling solutions and multiple exponential potentials

We present a phase-space analysis of cosmology containing multiple scalar fields with positive and negative exponential potentials. We show that there exist power-law multi-kinetic-potential scaling solutions for sufficiently flat positive potentials or steep negative potentials. The former is the unique late-time attractor and the well-known assisted inflationary solution, but the later is never unstable in an expanding universe. Moreover, for steep negative potentials there exist a kinetic-dominated regime in which each solution is a late-time attractor. We briefly discuss the physical consequences of these results.

Attractor solution of phantom field

In light of recent study on the dark energy models that manifest an equation of state $w<-1$, we investigate the cosmological evolution of phantom field in a specific potential, exponential potential in this paper. The phase plane analysis show that the there is a late time attractor solution in this model, which address the similar issues as that of fine tuning problems in conventional quintessence models. The equation of state $w$ is determined by the attractor solution which is dependent on the $\lambda$ parameter in the potential. We also show that this model is stable for our present observable universe.

Self-Similar Static Spherically Symmetric Scalar Field Models

Dynamical systems techniques are used to study the class of self-similar static spherically symmetric models with two non-interacting scalar fields with exponential potentials. The global dynamics depends on the scalar self-interaction potential parameters k1 and k2. For all values of k1, k2, there always exists (a subset of) expanding massless scalar field models that are early-time attractors and (a subset of) contracting massless scalar field models that are late-time attractors. When k1 ≥ 1/\(\sqrt 3 \) and k2 ≥ 1/\(\sqrt 3 \), in general the solutions evolve from an expanding massless scalar fields model and then recollapse to a contracting massless scalar fields model. When k1 < 1/\(\sqrt 3 \) or k2 < 1/\(\sqrt 3 \), the solutions generically evolve away from an expanding massless scalar fields model or an expanding single scalar field model and thereafter asymptote towards a contracting massless scalar fields model or a contracting single scalar field model. It is interesting that in this case a single scalar field model can represent the early-time or late-time asymptotic dynamical state of the models. The dynamics in the physical invariant set which constitutes a part of the boundary of the five-dimensional timelike self-similar physical region are discussed in more detail.

Cosmology with positive and negative exponential potentials

We present a phase-plane analysis of cosmologies containing a scalar field ϕ with an exponential potential V ∝ exp(−λ κ ϕ) where κ2 = 8πG and V may be positive or negative. We show that power-law kinetic–potential scaling solutions only exist for sufficiently flat (λ2 < 6) positive potentials or steep (λ2 > 6) negative potentials. The latter correspond to a class of ever-expanding cosmologies with negative potential. However, we show that these expanding solutions with a negative potential are unstable in the presence of ordinary matter, spatial curvature or anisotropic shear, and generic solutions always recollapse to a singularity. Power-law kinetic–potential scaling solutions are the late-time attractor in a collapsing universe for steep negative potentials (the ekpyrotic scenario) and stable against matter, curvature or shear perturbations. Otherwise kinetic-dominated solutions are the attractor during collapse (the pre-big-bang scenario) and are only marginally stable with respect to anisotropic shear.

Aspects of tachyonic inflation with an exponential potential

We consider issues related to tachyonic inflation with exponential potential. We find exact solution of evolution equations in the slow roll limit in FRW cosmology. We also carry out similar analysis in case of Brane assisted tachyonic inflation. We investigate the phase space behavior of the system and show that the dust like solution is a late time attractor. The difficulties associated with reheating in the tachyonic model are also indicated.