We identify the class of f(R) dark energy models which have a viable cosmology, i.e. a matter dominated epoch followed by a late-time acceleration. The deviation from a LambdaCDM model (f=R-Lambda) is quantified by the function m=Rf_{,RR}/f_{,R}. The matter epoch corresponds to m(r=-1) simeq +0 (where r=-Rf_{,R}/f) while the accelerated attractor exists in the region 0<m<1. We find that the equation of state w_DE of all such ``viable'' f(R) models exhibits two features: w_DE diverges at some redshift z_{c} and crosses the cosmological constant boundary (``phantom crossing'') at a redshift z_{b} smaller than z_{c}. Using the observational data of Supernova Ia and Cosmic Microwave Background, we obtain the constraint m<O(0.1) and we find that the phantom crossing could occur at z_{b}>1, i.e. within reach of observations. If we add local gravity constraints, the bound on m becomes very stringent, with m several orders of magnitude smaller than unity in the region whose density is much larger than the present cosmological density. The representative models that satisfy both cosmological and local gravity constraints take the asymptotic form m(r)=C(-r-1)^p with p>1 as r approaches -1.
Recently a lot of attention has been given to building dark energy models in which the equation-of-state parameter $w$ can cross the phantom divide $w=-1$. However, to our knowledge, these models with crossing the phantom divide only provide the possibility that $w$ can cross -1. They do not answer another question: {\em why crossing phantom divide occurs recently?} Since in many existing models whose equation-of-state parameter can cross the phantom divide, $w$ undulates around -1 randomly, {\em why are we living in an epoch $w<-1$?} This can be regarded as the second cosmological coincidence…
A class of braneworld models can lead to phantom-like acceleration of the late universe, but without the need for any phantom matter. In the simplest models, the universe contains only cold dark matter and a cosmological constant. We generalize these models by introducing a quintessence field. The new feature in our models is that quintessence leads to a crossing of the phantom divide, $w=-1$. This is a purely gravitational effect, and there is no phantom instability. Furthermore, the Hubble parameter is always decreasing, and there is no big rip singularity in the future.
We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (i.e., in the so-called Jordan frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (i.e., in the so-called Einstein frame) the singularity becomes the infinite-time one. Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitation…
The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is …
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 $w<-1$ 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 sing…
There is accumulating observational evidence (based on SnIa data) that the dark energy equation of state parameter $w$ may be evolving with time and crossing the phantom divide barrier $w=-1$ at recent times. The confirmation of these indications by future data would indicate that minimally coupled quintessence can not reproduce the observed expansion rate $H(z)$ for any scalar field potential. Here we explicitly demonstrate that scalar tensor theories of gravity (extended quintessence) can predict crossing of the phantom divide barrier. We reconstruct phenomenologically viable scalar-tensor p…
Considering the single scalar field models of dark energy, i.e. the quintessence and phantom models, it is shown that the quantum effects can cause the system crosses the w = -1 line. This phenomenon does not occur in classical level. The quantum effects are described via the account of conformal anomaly.
Hybrid Chaplygin gas model is put forward, in which the gases play the role of dark energy. For this model the coincidence problem is greatly alleviated. The effective equation of state of the dark energy may cross the phantom divide $w=-1$. Furthermore, the crossing behaviour is decoupled from any gravity theories. In the present model, $w<-1$ is only a transient behaviour. There is a de Sitter attractor in the future infinity. Hence, the big rip singularity, which often afflicts the models with matter whose effective equation of state less than -1, is naturally disappear. There exist stable …
We discuss the phenomenon of the smooth dynamical gravity induced crossing of the phantom divide line in a framework of simple cosmological models where it appears to occur rather naturally, provided the potential of the unique scalar field has some kind of cusp. The behavior of cosmological trajectories in the vicinity of the cusp is studied in some detail and a simple mechanical analogy is presented. The phenomenon of certain complementarity between the smoothness of the spacetime geometry and matter equations of motion is elucidated. We introduce a network of cosmological histories and qual…
We investigate general braneworld models, with a non-minimally coupled phantom bulk field and arbitrary brane and bulk matter contents. We show that the effective dark energy of the brane-universe acquires a dynamical nature, as a result of the non-minimal coupling which provides a mechanism for an indirect "bulk-brane interaction" through gravity. For late-time cosmological evolution and without resorting to special ansatzes or to specific areas of the parameter space, we show that the -1-crossing of its equation-of-state parameter is general and can be easily achieved. As an example we provi…
Simple scalar field cosmological models are considered describing gravity assisted crossing of the phantom divide line. This crossing or (de)-phantomization characterized by the change of the sign of the kinetic term of the scalar field is smooth and driven dynamically by the Einstein equations. Different cosmological scenarios, including the phantom phase of matter are sketched.
We investigate models of dark energy with purely kinetic multiple k-essence sources that allow for the crossing of the phantom divide line, without violating the conditions of stability. It is known that with more than one kinetic k-field one can possibly construct dark energy models whose equation of state parameter $\wx$ crosses -1 (the phantom barrier) at recent red-shifts, as indicated by the Supernova Ia and other observational probes. However, such models may suffer from cosmological instabilities, as the effective speed of propagation $\cx$ of the dark energy density perturbations may b…
We consider fluid perturbations close to the "phantom divide" characterised by p = -rho and discuss the conditions under which divergencies in the perturbations can be avoided. We find that the behaviour of the perturbations depends crucially on the prescription for the pressure perturbation delta-p. The pressure perturbation is usually defined using the dark energy rest-frame, but we show that this frame becomes unphysical at the divide. If the pressure perturbation is kept finite in any other frame, then the phantom divide can be crossed. Our findings are important for generalised fluid dark…
We discuss a class of phantom ($p < - \varrho$) cosmological models. Except for phantom we admit various forms of standard types of matter and discuss the problem of singularities for these cosmologies. The singularities are different from those of standard matter cosmology since they appear for infinite values of the scale factor. We also find an interesting relation between the phantom models and standard matter models which is like the duality symmetry of string cosmology.
Smooth double crossing of the phantom barrier $w_Λ = -1$ has been found possible in cosmological model with Gauss-Bonnet-scalar interaction, in the presence of background cold dark matter. Such crossing has been observed to be a sufficiently late time phenomena and independent of the sign of Gauss-Bonnet-scalar interaction. The luminosity distance versus redshift curve shows a perfect fit with the $ΛCDM$ model up to $z=3.5$.
We study quintessence and phantom field theory models based on linear-negative potentials of the form $V(ϕ)=s ϕ$. We investigate the predicted redshift dependence of the equation of state parameter $w(z$ for a wide range of slopes $s$ in both quintessence and phantom models. We use the gold dataset of 157 SnIa and place constraints on the allowed range of slopes $s$. We find $s=0\pm 1.6$ for quintessence and $s=\pm 0.7\pm 1$ for phantom models (the range is at the $2σ$ level and the units of $s$ are in $\sqrt{3}M_p H_0^2\simeq 10^{-38}eV^3$ where $M_p$ is the Planck mass). In both cases the be…
If the dark energy equation of state parameter w(z) crosses the phantom divide line w=-1 (or equivalently if the expression d(H^2(z))/dz - 3Ω_m H_0^2 (1+z)^2 changes sign) at recent redshifts, then there are two possible cosmological implications: Either the dark energy consists of multiple components with at least one non-canonical phantom component or general relativity needs to be extended to a more general theory on cosmological scales. The former possibility requires the existence of a phantom component which has been shown to suffer from serious theoretical problems and instabilities. Th…
Dark energy cosmologies with an equation of state parameter $w$ less than -1 are often found to violate the null energy condition and show unstable behaviour. A solution to this problem may require the existence of a consistent effective theory that violates the null energy condition only momentarily and does not develop any instabilities or other pathological features for a late time cosmology. A model which incorporates a dynamical scalar field $ϕ$ coupled to the quadratic Riemann invariant of the Gauss-Bonnet form is a viable proposal. Such an effective theory is shown to admit nonsingular …
We consider multiple k-essence sources and obtain the conditions their kinetic functions must satisfy so that purely kinetic k-essences lead to models with phantom barrier crossing. After that, we show that polynomial kinetic functions allow the integration of the dynamical equations determining the geometry and the k-fields. The models thus obtained have accelerated expansion at late cosmic time, representing universes ending at a finite time with a big rip singularity. In addition, these models begin to evolve from an initial singularity, so they have a finite time span.
In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model whit cosmological constant, containing a stiff fluid and a classical Dirac field. The proposed cosmological scenario describes the evolution of effective dark matter and dark energy components reproducing, with the help of that effective multifluid configuration, the quintessential behavior. We find the value of the scale factor where the effective dark energy component crosses the phantom divide. The model we introduce, which can be considered as a modified $\La$CDM one, is characterized by a set of…
By the assumption that the thermodynamics second law is valid, we study the possibility of $ω=-1$ crossing in interacting holographic dark energy model. Depending on the choice of the horizon and the interaction, the transition from quintessence to phantom regime and subsequently from phantom to quintessence phase may be possible. The second transition avoids the big rip singularity. We compute the dark energy density at transition time and show that by choosing appropriate parameters we can alleviate the coincidence problem.
We construct a new brane-world model composed of a bulk -with a dilatonic field-, plus a brane -with brane tension coupled to the dilaton-, cold dark matter and an induced gravity term. It is possible to show that depending on the nature of the coupling between the brane tension and the dilaton this model can describe the late-time acceleration of the brane expansion (for the normal branch) as it moves within the bulk. The acceleration is produced together with a mimicry of the crossing of the cosmological constant line (w=-1) on the brane, although this crossing of the phantom divide is obtai…
We consider the Randall-Sundrum brane-world model with bulk-brane energy transfer where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. It is remarkable that these curvature terms will not change the dynamics of the brane universe at low energy. Parameterizing the energy transfer and taking the dark radiation term into account, we find that the phantom divide of the equation of state of effective dark energy could be crossed, without the need of any …
Dark energy constraints have forced viable alternatives that differ substantially from a cosmological constant Lambda to have an equation of state w that evolves across the phantom divide set by Lambda. Naively, crossing this divide makes the dark energy gravitationally unstable, a problem that is typically finessed by unphysically ignoring the perturbations. While this procedure does not affect constraints near the favored cosmological constant model it can artificially enhance the confidence with which alternate models are rejected. Similar to the general problem of stability for w< 0, the s…
The dark energy crossing of the cosmological constant boundary (the transition between the quintessence and phantom regimes) is described in terms of the implicitly defined dark energy equation of state. The generalizations of the models explicitly constructed to exhibit the crossing provide the insight into the cancellation mechanism which makes the transition possible.
Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic acceleration provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well controlled approximation for a wide range of "smooth" dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well ab…
Singularities in the dark energy late universe are discussed, under the assumption that the Lagrangian contains the Einstein term R plus a modified gravity term of the form R^α, where αis a constant. It is found, similarly as in the case of pure Einstein gravity [I. Brevik and O. Gorbunova, Gen. Rel. Grav. 37 (2005), 2039], that the fluid can pass from the quintessence region (w>-1) into the phantom region (w<-1) as a consequence of a bulk viscosity varying with time. It becomes necessary now, however, to allow for a two-fluid model, since the viscosities for the two components vary differentl…
We show that phantom dark energy, if it is described by a K-essence theory, has three fundamental problems: first, its hamiltonian is unbounded from below. Second, classical stability precludes the equation of state from crossing the ``Lambda-barrier'', $w_Λ=-1$. Finally, both the equation of state and the sound speed are unbounded -- the first, from below, the second, from above -- if the kinetic term is not bounded by dynamics.
Inhomogeneous cosmological models have recently become a very interesting alternative to standard cosmology. This is because these models are able to fit cosmological observations without the need for dark energy. However, due to inhomogeneity and pressure-less matter content, these models can suffer from shell crossing singularities. These singularities occur when two shell of dust collide with each other leading to infinite values of the density. In this Letter we show that if inhomogeneous pressure is included then these singularities can be prevented from occurring over the period of struc…
We investigate canonical, phantom and quintom models, with the various fields being non-minimally coupled to gravity, in the framework of holographic dark energy. We classify them and we discuss their cosmological implications. In particular, we examine the present value of the dark energy equation-of-state parameter and the crossing through the phantom divide, and we extract the conditions for a future cosmological singularity. The combined scenarios are in agreement with observations and reveal interesting cosmological behaviors.
Smooth double crossing of the phantom divide line $w_Λ=-1$ has been found possible with a single minimally coupled scalar field for the most simple form of generalized k-essence cosmological model, in the presence of background cold dark matter. Such crossing is a sufficiently late time transient phenomena and does not have any pathological behaviour.
We present a model independent method of reconstructing the Lagrangian for the k-essence field driving the present acceleration of the universe. We consider the simplest k-essence model for which the potential is constant. Later we use three parametrizations for the Hubble parameter $H(z)$, consistent with the recent SN1a data, to yield the Lagrangian $F$. Our reconstruction program does not generate any physically realistic Lagrangian for models that allow phantom crossing, whereas models without phantom crossing, yield well behaved Lagrangian.
