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 become {\it imaginary} while the $\wx = -1$ barrier is crossed. Working out the expression for $\cx$ we show that multiple kinetic k-essence fields do indeed lead to a $\wx = -1$ crossing dark energy model, satisfying the stability criterion $\cx^2 \geq 0$ as well as the condition $\cx \leq 1$ (in natural units), which implies that the dark energy is not super-luminal. As a specific example, we construct a phantom barrier crossing model involving three k-fields for which $\cx$ is a constant, lying between 0 and 1. The model fits well with the latest Supernova Ia Union data, and the best fit shows that $\wx$ crosses -1 at red-shift $z \sim 0.2$, whereas the dark energy density nearly tracks the matter density at higher red-shifts.
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.
We devise a method to obtain a phantom version of FRW k-essence cosmologies with homogeneous k-fields by applying form-invariance transformations. It can be seen that the transformation performs the maps $H\toH$ and $ρ+p\to-(ρ+p)$, which in turn give $γ\toγ$ and $a\to a^{-1}$. The discussion is presented in a general setup, valid for FRW k-essence cosmologies, and then we discuss power-law solutions for illustration purposes. First, we deal with models such that the gradient of the k-field is not constant, which include standard and generalized tachyon cosmologies. We concentrate on the usual …
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 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.
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 …
We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that 1.Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and Hamiltonian constraints of General Relativity, can be easily constructed. 2. The physical time evolution of those observables is generated by a natural physical Hamiltonian which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kuchař. In order that the physical Hamiltonian is clos…
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.
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…
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…
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 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…
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.
Although generalized Chaplygin phantom models do not show any big rip singularities, we investigated k-essence models together with noncanonical kinetic energy for which there might be a big rip future singularity in the phantom region. We present our results by finely tuning the parameter ($β$) which is closely related to the canonical kinetic term in $k$-essence formalism. The scale factor $a(t)$ could be negative and decreasing within a specific range of $β$ during the initial evolutional period. There will be no singularity for the scale factor for all times once $β$ is carefully selected.
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…
We discuss thermodynamic properties of dark energy using the formalism of field theory at finite temperature. In particular, we apply our formalism to a purely kinetic type of k-essence. We show quite generally that the entropy associated with dark-energy is always equal or greater than zero. Hence, contrary to often stated claims, a violation of the null energy condition (phantom dark energy) does not necessarily yield a negative entropy. In addition, we find that the thermal fluctuations of a k-essence field may be represented by a free boson gas with an effective number of degrees of freedo…
The result from the SN1a projects suggest that the dark energy can be represented by a fluid with w<-1. However, it is commonly argued that a fluid with |w|>1 contradicts causality. Here, we will show that a fluid with |w|>1 does not contradict causality if $w$ is not constant. Scalar field are the most promising candidates for describing the dark energy and they do not have a constant equation of state parameter w. Scalar potentials may lead to regions where w is larger or smaller than one and even regions where the group velocity $d p/dρ$ diverges. We study the evolution of scalar field pert…
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 …
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 $z=3.5$.
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 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…
Cosmological scaling solutions are particularly important in solving the coincidence problem of dark energy. We derive the equations of sub-Hubble linear matter perturbations for a general scalar-field Lagrangian--including quintessence, tachyon, dilatonic ghost condensate and k-essence--and solve them analytically for scaling solutions. We find that matter perturbations are always damped if a phantom field is coupled to dark matter and identify the cases in which the gravitational potential is constant. This provides an interesting possibility to place stringent observational constraints on s…
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…
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…
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…
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…
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…
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…
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 …
In the present work, the Brans-Dicke theory of gravity is taken as a possible theory of k-essence coupled to gravity and then the role played by the Brans-Dicke scalar field in relation to the unified model for dark matter and dark energy is explored. It has been realized that the BD scalar field does indeed play a role of a k-essence, but in a very unique way which distinguishes it from other k-essence fields studied in the literature such as the (generalized) Chaplygin gas or the purely kinetic k-essence studied recently by Scherrer. That is, instead of providing an interpolation between the…
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…
We study generic single-field dark energy models, by a parametrization of the most general theory of their perturbations around a given background, including higher derivative terms. In appropriate limits this approach reproduces standard quintessence, k-essence and ghost condensation. We find no general pathology associated to an equation of state w_Q < -1 or in crossing the phantom divide w_Q = -1. Stability requires that the w_Q < -1 side of dark energy behaves, on cosmological scales, as a k-essence fluid with a virtually zero speed of sound. This implies that one should set the speed of s…
In the framework of the scale invariant model of the Two Measures Field Theory (TMT), we study the dilaton-gravity sector in the context of spatially flat FRW cosmology. The scale invariance is spontaneously broken due to the intrinsic features of the TMT dynamics. If no fine tuning is made, the effective $ϕ$-Lagrangian $p(ϕ,X)$ depends quadratically upon the kinetic term $X$. Hence TMT represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the underlying action intended for obtaining this result. Depending of the choice of regions …
A class of solutions for phantom field corresponding to a generalized k-essence lagrangian has been presented, employing a simple method which provides the scope to explore many such. All the solutions having dynamical state parameter are found to touch the magic line w = -1, asymptotically. The solutions with constant equation of state can represent phantom, quitessence or an ordinary scalar field cosmologies depending on the choice of a couple of parameters of the theory. For w approximately equal to -1, quintessence and phantom models are indistinguishable through the Hubble parameter. Fina…
In spite of its rather weird properties which include violation of the dominant-energy condition, the requirement of superluminal sound speed and increasing vacuum-energy density, phantom energy has recently attracted a lot of scientific and popular interests. In this letter it is shown that in the framework of a general k-essence model, vacuum-phantom energy leads to a cosmological scenario having negative sound speed and a big-rip singularity, where the field potential also blows up, which might occur at an almost arbitrarily near time in the future that can still be comfortably accommodated…
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.
In this work, we consider time-dependent dark energy star models, with an evolving parameter $ω$ crossing the phantom divide, $ω=-1$. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark energy star into a wormhole. The criteria for this topology change are discussed, in particular, we consider the Morse Index analysis and a Casimir energy a…
The unifying approach to early-time and late-time universe based on phantom cosmology is proposed. We consider gravity-scalar system which contains usual potential and scalar coupling function in front of kinetic term. As a result, the possibility of phantom-non-phantom transition appears in such a way that universe could have effectively phantom equation of state at early time as well as at late time. In fact, the oscillating universe may have several phantom and non-phantom phases. As a second model we suggest generalized holographic dark energy where infrared cutoff is identified with combi…
By choosing the future event horizon as the horizon of the flat FLRW universe, we show that although the interacting holographic dark energy model is able to explain the phantom divide line crossing, but the thermodynamics second law is not respected in this model. We show that if one takes the particle event horizon as the horizon of the universe, besides describing $ω=-1$ crossing in a consistent way with thermodynamics second law, he is able to determine appropriately the ratio of dark matter to dark energy density at transition time. In this approach, after the first transition from quinte…
One of the puzzles of the dark energy problem is the (first) cosmological coincidence problem, namely, {\em why does our universe begin the accelerated expansion recently? why are we living in an epoch in which the dark energy density and the dust matter energy density are comparable?} On the other hand, cosmological observations hint that the equation-of-state parameter (EoS) of dark energy crossed the phantom divide $w_{de}=-1$ in the near past. Many dark energy models whose EoS can cross the phantom divide have been proposed. However, to our knowledge, these models with crossing the phantom…
Phantom fields with negative kinetic energy are often plagued by the vacuum quantum instability in the ultraviolet region. We present a Lorentz-violating dark energy model free from this problem and show that the crossing of the cosmological constant boundary w=-1 to the phantom equation of state is realized before reaching a de Sitter attractor. Another interesting feature is a peculiar time-dependence of the effective Newton's constant; the magnitude of this effect is naturally small but may be close to experimental limits. We also derive momentum scales of instabilities at which tachyons or…
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.
Recently a lot of attention has been drawn to build dark energy model in which the equation-of-state parameter $w$ can cross the phantom divide $w=-1$. One of models to realize crossing the phantom divide is called quintom model, in which two real scalar fields appears, one is a normal scalar field and the other is a phantom-type scalar field. In this paper we propose a non-canonical complex scalar field as the dark energy, which we dub ``hessence'', to implement crossing the phantom divide, in a similar sense as the quintom dark energy model. In the hessence model, the dark energy is describe…
We consider a braneworld model with bulk-brane energy exchange. This allows for crossing of the w=-1 phantom divide line without introducing phantom energy with quantum instabilities. We use the latest SnIa data included in the Gold06 dataset to provide an estimate of the preferred parameter values of this braneworld model. We use three fitting approaches which provide best fit parameter values and hint towards a bulk energy component that behaves like relativistic matter which is propagating in the bulk and is moving at a speed v along the fifth dimension, while the bulk-brane energy exchange…
In this letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system and analyze it on a invariant 2-dimensional submanifold. Then the concordance FRW model with the cosmological constant $Λ$ is a global attractor situated on a 2-dimensional invariant space. We also study the behaviour near this attractor, which can be approximated by the dynamics of the linearized part of the system. We demonstrate that trajectories of the …
We carry out a Bayesian model selection analysis of different dark energy parametrizations using the recent luminosity distance data of high redshift supernovae from Riess et al. 2007 and from the new ESSENCE Supernova Survey. Including complementary cosmological datasets, we found substantial evidence ($Δ\ln (E) \sim 1$) against a time-varying dark energy equation of state parameter, and against phantom dark energy models. We find a small preference for a standard cosmological constant over accelerating non-phantom models where w is constant, but allowed to vary in the range -1 to -0.33.
A new class of braneworld models displaying late-time phantom acceleration without resorting to a phantom fluid is presented. In this scenario expansion is fuelled by dark matter together with some effective dark energy capable of crossing the phantom divide. Unlike a previous proposal of this nature, in these models the effective phantom behaviour remains valid at all redshifts for some choices of the free parameters of the models. The construction is based on the generalised Chaplygin gas, and the cosmological history interpolates between a standard CDM-like behaviour at early times and a de…
