We review a dynamical dark energy model scarcely studied in the literature and we introduce two possible generalizations. We discuss separately the behavior of the original model and a minimal extension of it by exploring some early and late times limits, we find that the cosmic components are related by their parameters state. In order to have access to the phantom regime we present two dark energy densities inspired from the holographic approach and from the emergent entropic forces model in the early universe. For the first case we obtain a Type III singularity and in the second proposal we have a transition from decelerated to accelerated cosmic expansion that starts as phantom type. However, the final stage of the universe is a de Sitter state.
We find the group of symmetry transformations generated by interacting fluids in spatially flat Friedmann-Robertson-Walker (FRW) spacetime which links cosmologies with the same scale factor {\it (identity)} or with scale factors $a$ and $a^{-1}$ {\it (duality)}. There exists a duality between contracting and superaccelerated expanding scenarios associated with {\it (phantom)} cosmologies. We investigate the action of this symmetry group on self-interacting minimally(conformally) coupled quintessence and $k$-essence cosmologies.
Form invariance transformations can be used for constructing phantom cosmologies starting with conventional cosmological models. In this work we reconsider the scalar field case and extend the discussion to fermionic fields, where the "phantomization" process exhibits a new class of possible accelerated regimes. As an application we analyze the cosmological constant group for a fermionic seed fluid.
We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.
We illustrate how form-invariance transformations can be used for constructing phantom cosmologies from standard scalar field universes. First, we discuss how to relate two flat Friedmann-Robertson-Walker cosmologies with different barotropic indexes $γ$ and $\bar γ$. Then, we consider the particular case $\bar γ=-γ$, and we show that if the matter content is interpreted in terms of self-interacting scalar fields, then the corresponding transformation provides the link between a standard and a phantom cosmology. After that, we illustrate the method by considering models with exponential potent…
The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in particular, for the Sine-Gordon potential.
We study the structural stability of a cosmic acceleration (inflation) in a class of k-essence cosmologies against changes in the shape of the potential. Those models may be viewed as generalized tachyon cosmologies and this analysis extends previous results on the structural stability of cosmic acceleration in tachyon cosmologies. The study considers both phantom and non-phantom cases. The concepts of rigidity and fragility are defined through a condition on the functional form of the Hubble factor. Given the known result of the existence of inflationary (non-phantom) and super-inflationary (…
In the classical relativistic regime, the accretion of phantom energy onto a black hole reduces the mass of the black hole. In this context, we have investigated the evolution of a Schwarzschild black hole in the standard model of cosmology using the phantom-like modified variable Chaplygin gas and the viscous generalized Chaplygin gas. The corresponding expressions for accretion time scale and evolution of mass have been derived. Our results indicate that mass of the black hole will decrease if the accreting phantom Chaplygin gas violates the dominant energy condition and will increase in the…
We consider the classical linear stability of a static universe filled with a non-interacting mixture of isotropic radiation and a ghost scalar field. Unlike the conventional Einstein static model, this cosmology is stable against homogeneous and isotropic perturbations. This is shown by means of exact oscillatory solutions about the original static state. We also examine the linear response of the static ghost universe to all types of inhomogeneous fluctuations, namely density, vorticity and gravitational-wave perturbations. The results show that the static background constrains the linear ev…
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.
We present a general algorithm based on the concept of form-invariance which can be used for generating phantom cosmologies. It involves linear transformations between the kinetic energy and the potential of the scalar field, and transforms solutions of the Einstein-Klein-Gordon equations which preserve the weak energy condition into others which violate it, while keeping the energy density of the field positive. All known solutions representing phantom cosmologies are unified by this procedure. Using the general algorithm we obtain those solutions and show the relations between them. In addit…
We discuss the particle horizon problem in the framework of spatially homogeneous and isotropic scalar cosmologies. To this purpose we consider a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime with possibly non-zero spatial sectional curvature (and arbitrary dimension), and assume that the content of the universe is a family of perfect fluids, plus a scalar field that can be a quintessence or a phantom (depending on the sign of the kinetic part in its action functional). We show that the occurrence of a particle horizon is unavoidable if the field is a quintessence, the spatial curvature…
It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole \textit{only} when the Ellis solution parameter $γ$ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequ…
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 …
Within the theory of the ghost-free bigravity, we present the most general cosmological solution for which the physical metric is homogeneous and isotropic, while the second metric is inhomogeneous. The solution includes a matter source and exists for any values of the theory parameters. The physical metric describes a universe with the late time acceleration due to the effective cosmological term mimicked by the graviton mass. When perturbed, this universe should rest approximately homogeneous and isotropic in space regions small compared to the graviton Compton length. In the limit where the…
The dynamics of a minimally coupled scalar field in the expanding universe is discussed with special reference to phantom cosmology. The evolution of the universe with a phantom field vis-a-vis a quintessence field is compared. Phantom cosmologies are found to have two special features i) occurrence of a singularity where the scale factor, the energy density and Ricci curvature scalar diverge to infinity. This singularity occurs at a finite time, depending on w during cosmic evolution, ii) degeneracy in the determination of w(z_m) for a particular transition redshift z_m which seems to impart …
It is shown that any spatially flat and isotropic universe undergoing accelerated expansion driven by a self-interacting scalar field can be directly related to a contracting, decelerating cosmology. The duality is made manifest by expressing the scale factor and Hubble parameter as functions of the scalar field and simultaneously interchanging these two quantities. The decelerating universe can be twinned with a cosmology sourced by a phantom scalar field by inverting the scale factor and leaving the Hubble parameter invariant. The accelerating model can be related to the same phantom univers…
In this paper we establish dualities between inflationary, cyclic/ekpyrotic, and phantom cosmologies within the patch formalism approximating high-energy effects in scenarios with extra dimensions. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts; the dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane. We then address some qualitative issues about phantomlike cosmologies without phantom matter.
We study analytically and numerically the evolution of bound systems in universes with accelerating expansion where the acceleration either increases with time towards a Big Rip singularity (phantom cosmologies) or decreases with time (quintessence). We confirm the finding of Caldwell et. al. [arXiv:astro-ph/0302506] (hereafter CKW) that bound structures get dissociated in phantom cosmologies but we demonstrate that this happens earlier than anticipated by CKW. In particular we find that the `rip time' when a bound system gets unbounded is not the time when the repulsive phantom energy gravita…
The recently proposed infrared modification of gravity through the introduction of a ghost scalar field results in a number of interesting cosmological and phenomenological implications. In this paper, we derive the exact cosmological solutions for a number of scenarios where at late stages, the ghost behaves like dark matter, or dark energy. The full solutions give valuable information about the non-linear regime beyond the asymptotic first order analysis presented in the literature. The generic feature is that these ghost cosmologies give rise to smooth transitions between radiation dominate…
We present a novel dark energy candidate, based upon the existence and dynamics of Ghost D-branes in a warped compactification of type IIB string theory. Gp-branes cancel the combined BPS sectors of the Dp-branes, while they preserve the same supersymmetries. We show that this scenario can naturally lead to either quintessence or phantom-like behaviors, depending on the form of the involved potentials and brane tension.
We discuss a more general class of phantom ($p < -\varrho$) cosmologies with various forms of both phantom ($w < -1$), and standard ($w > -1$) matter. We show that many types of evolution which include both Big-Bang and Big-Rip singularities are admitted and give explicit examples. Among some interesting models, there exist non-singular oscillating (or "bounce") cosmologies, which appear due to a competition between positive and negative pressure of variety of matter content. From the point of view of the current observations the most interesting cosmologies are the ones which start with a Big…
The Nine-Year WMAP results combined with other cosmological data seem to indicate an enhanced favor for the phantom regime, comparing to previous analyses. This behavior, unless reversed by future observational data, suggests to consider the phantom regime more thoroughly. In this work we provide three modified gravitational scenarios in which we obtain the phantom realization without the appearance of ghosts degrees of freedom, which plague the naive approaches on the subject, namely the Brans-Dicke type gravity, the scalar-Einstein-Gauss-Bonnet gravity, and the $F(R)$ gravity, which are more…
We present the detailed derivation of the recently announced most general cosmological solution with homogeneous and isotropic metric in the ghost-free massive gravity theory. We use the standard parametrization of the theory in terms of the matrix square root, and then show how the same results are recovered within the tetrad formulation. The solution obtained includes the matter source, it exists for generic values of the theory parameters, and it describes a universe that can be spatially open, closed, or flat, and that shows the late time acceleration due to the effective cosmological term…
Three static models with two interacting phantom and ghost scalar fields were considered: a model of a traversable wormhole, a brane-like model and a spherically symmetric problem. It was shown numerically that regular solutions exist for all three cases.
We investigate a simple braneworld model in which the universe contains only cold dark matter and a cosmological constant, but the effective dark energy is phantom-like because of extra-dimensional gravity effects. Modified gravity screens the cosmological constant Lambda, allowing for a larger Lambda. In practice, observations do not favour any significant screening. We use supernova data, the cosmic microwave background shift parameter, and the baryon oscillation peak in the galaxy distribution to constrain the model. We find the mean value of Omega_m with 68% confidence limits, and an upper…
Up-to-date cosmological data analyses have shown that \textit{(a)} a closed universe is preferred by the Planck data at more than $99\%$ CL, and \textit{(b)} interacting scenarios offer a very compelling solution to the Hubble constant tension. In light of these two recent appealing scenarios, we consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of state in both the quintessential and phantom regimes. When considering Cosmic Microwave Background data only, a phantom and closed universe can perfectly …
In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $Λ$CDM\, and $Λ$DGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the $f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in t…
Cosmological fluids with a Generalized Equation of State (GEoS) are here considered, whose corresponding EoS parameter $ω$ describes a fluid with phantom behavior, namely $ω<-1$, but leading to universes free of singularities at any past or future, finite time. Thus avoiding, in particular, the Big Bang and the Big Rip singularities, the last one considered to be typical in phantom fluid models. More specifically, such GEoS fluid cosmologies lead to regular Little Rip universes. A remarkable new property of these solutions is proven here, namely that they avoid the initial singularity at early…
We present a survey of the known cosmological and black hole solutions in ghost-free bigravity and massive gravity theories. These can be divided into three classes. First, there are solutions with proportional metrics, which are the same as in General Relativity with a cosmological term, which can be positive, negative or zero. Secondly, for spherically symmetric systems, there are solutions with non-bidiagonal metrics. The g-metric fulfills Einstein equations with a positive cosmological term and a matter source, while the f-metric is anti-de Sitter. The third class contains solutions with b…
We investigate the stability against inhomogeneous perturbations and the appearance of ghost modes in Gauss-Bonnet gravitational theories with a non-minimally coupled scalar field, which can be regarded as either the dilaton or a compactification modulus in the context of string theory. Through cosmological linear perturbations we extract four no-ghost and two sub-luminal constraint equations, written in terms of background quantities, which must be satisfied for consistency. We also argue that, for a general action with quadratic Riemann invariants, homogeneous and inhomogeneous perturbations…
We investigate the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity. First, we study the non-interacting generalized ghost dark energy in a flat Friedmann-Robertson-Walker (FRW) background. We obtain the equation of state parameter, $w_D=p/ρ$, the deceleration parameter, and the evolution equation of the generalized ghost dark energy. We find that, in this case, $w_D$ cannot cross the phantom line ($w_D>-1$) and eventually the universe approaches a de-Sitter phase of expansion $(w_D\rightarrow-1)$. Then, we extend the study to the interac…
The proposal of pilgrim dark energy is based on the speculation that phantom-like dark energy possesses enough resistive force to preclude the black hole formation in the later universe. We explore this phenomenon by assuming the generalized ghost version of pilgrim dark energy. We find that most of the values of the interacting ($ξ^2$) as well as pilgrim dark energy ($u$) parameters push the equation of state parameter towards phantom region. The squared speed of sound shows that this model remains stable in most of the cases of $ξ^2$ and $u$. We also develop $ω_Λ-ω'_Λ$ plane and observe that…
We consider the kinematical and dynamical evolution of Friedmann universes with a mixture of non-interacting matter and a ghost-like field, in a scenario analogous to that advocated by the Quintom model. Assuming that the conventional matter dominates today, we find that the ghost component can bring the future expansion and the past contraction of the model to a finite halt. Moreover, at the moment the expansion or contraction stops, we find that the tendency of the universe is to bounce back and re-collapse or re-expand. Therefore, the presence of a (never dominant) ghost-field with negative…
A class of dynamical dark energy models is constructed through an extended version of fermion fields corresponding to phantom dark ghost spinors, which are spin one half with mass dimension one. We find that if these spinors interact with torsion fields in a homogeneous and isotropic universe, then it does not imply any future dark energy singularity or any abrupt event, though the fermion has a negative kinetic energy. In fact, the equation of state of this dark energy model will asymptotically approach the value $w=-1$ from above without crossing the phantom divide and inducing therefore a d…
We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields, describing traversable wormholes with flat and AdS asymptotics and regular black holes, in particular, black universes. (A black universe is a regular black hole with an expanding, asymptotically isotropic space-time beyond the horizon.) Such objects exist in the presence of scalar fields with negative kinetic energy ("phantoms", or "ghosts"), which are not observed under usual physical conditions. To account for that, we consider what we call…
It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(Φ)$ is everywhere positive and the scalar field $Φ$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(Φ)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions…
We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields describing traversable wormholes with flat and AdS asymptotics and regular black holes, in particular, black universes. (A black universe is a regular black hole with an expanding, asymptotically isotropic space-time beyond the horizon.) The existence of such objects requires invoking scalars with negative kinetic energy ("phantoms", or "ghosts"), which are not observed under usual physical conditions. To account for that, the so-called "trappe…
Chiellini-Integrable Cosmologies with Phantom Divide Crossing
School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院）；Centre for Theoretical Physics and Natural Philosophy, Nakhonsawan Studiorum for Advanced Studies, Mahidol University（马希隆大学那空沙旺高级研究学院理论与自然哲学中心）
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
In a homogeneous and isotropic universe bulk viscosity is the unique viscous effect capable to modify the background dynamics. Effects like shear viscosity or heat conduction can only change the evolution of the perturbations. The existence of a bulk viscous pressure in a fluid, which in order to obey to the second law of thermodynamics is negative, reduces its effective pressure. We discuss in this study the degeneracy in bulk viscous cosmologies and address the possibility that phantom dark energy cosmology could be caused by the existence of non-equilibrium pressure in any cosmic component.…
In this work, we reconstruct the $f(R)$ modified gravity for different ghost and generalized ghost dark energy models in FRW flat universe, which describe the accelerated expansion of the universe. The equation of state of reconstructed $f(R)$ - gravity has been calculated. We show that the corresponding $f(R)$ gravity of ghost dark energy model can behave like phantom or quintessence. We also show that the equation of state of reconstructed $f(R)$ gravity for generalized ghost model can transit from quintessence regime to the phantom regime as indicated by recent observations.
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 …
Two cosmological models with non-phantom matter having the same expansion of the universe as phantom cosmologies are constructed. The first model is characterized by the evolving gravitational "constant" $G$ and a dark energy component with a non-conserved energy-momentum tensor. The second model includes two interacting components, the dark energy component and the matter component. Closed form solutions are obtained for the constant values of model parameters and constraints on the parameters of each model from cosmological observations are outlined. For both models it is explicitly shown ho…
We reconstruct $f(R,T)$ theory (where $R$ is the scalar curvature and $T$ is the trace of energy-momentum tensor) in the framework of QCD ghost dark energy models. In this study, we concentrate on particular models of $f(R,T)$ gravity which permits the standard continuity equation in this theory. It is found that reconstructed function can represent phantom and quintessence regimes of the universe in the background of flat FRW universe. In addition, we explore the stability of ghost $f(R,T)$ models.
Regarding the Veneziano ghost of QCD and its generalized form, we consider a Friedmann-Robertson-Walker (FRW) universe filled by a pressureless matter and a dark energy component interacting with each other through a mutual sign-changeable interaction of positive coupling constant. Our study shows that, at the late time, for the deceleration parameter we have $q\rightarrow-1$, while the equation of state parameter of the interacting ghost dark energy (GDE) does not cross the phantom line, namely $ω_D\geq-1$. We also extend our study to the generalized ghost dark energy (GGDE) model and show th…
It is well known that for spatially flat FRW cosmologies, the holographic dark energy disfavours the Hubble parameter as a candidate for the IR cutoff. For overcoming this problem, we explore the use of this cutoff in holographic ellipsoidal cosmological models, and derive the general ellipsoidal metric induced by a such holographic energy density. Despite the drawbacks that this cutoff presents in homogeneous and isotropic universes, based on this general metric, we developed a suitable ellipsoidal holographic cosmological model, filled with a dark matter and a dark energy components. At late…
The 6D braneworld with the phantom-like bulk scalar field is considered. We demonstrate pure gravitational localization of scalar field zero modes on the brane.
Rip cosmological models have been investigated in the framework of $f(T,\mathcal{T})$ theory of gravity, where $T$ denotes the torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor. These phantom cosmological models revealed that at initial epoch a EoS parameter $ω<-1$ and tends asymptotically at late phase to $-1$ $(ω\rightarrow -1)$. On the other hand, Wormhole Solutions and Big Trip have been subject of an investigation. The wormhole throat radius $R(t)$ and the conditions to be satisfied so that produces the Big Trip phenomenon have been discussed.
A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. Such models have been previously found as solutions of general relativity with a phantom scalar field as a source of gravity and, without phantoms, in a brane world of RS2 type. Here we construct examples of static, spherically symmetric black-universe solutions in general relativity with a minimally coupled scalar field ϕwhose kinetic energy is negative in a restricted strong-field region of space-time and positive outside it. Thus in such configurations a "ghost" …
We study phantom and inflationary cosmologies using form-invariance transformations of the Einstein equations with respect to $ρ$, $H$, $a$ and $p$, from a 5D vacuum. Equations of state and squared fluctuations of the inflaton and phantom fields are examined.
Exploring the accelerated expansion of the universe, we investigate the generalized ghost dark energy (GGDE) model from the statefinder diagnosis analysis in a flat FRW universe. First we calculate the cosmological evolution and statefinder trajectories for non-interacting case and then extend this work by considering the interaction between dark matter and dark energy components. We show that in the non-interacting case the phantom line can not be crossed and also he evolutionary trajectories of model in $s-r$ plane can not be discriminated. It has been shown that the present location of mode…
We illustrate how the group of symmetry transformations, which preserve the form of the n--dimensional flat Friedmann--Robertson--Walker cosmologies satisfying Einstein equations, acts in any dimension. This group relates the energy density and the isotropic pressure of the cosmic fluid to the expansion rate. The freedom associated with the dimension of the space time yields assisted inflation even when the energy density of the fluid is a dimensional invariant and enriches the set of duality transformations leading to phantom cosmologies.
We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a $Λ$-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the $Λ$-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the $Λ$-term and matter are screened at all times but there are nevertheless the early and lat…
It was argued that the vacuum energy of the Veneziano ghost field of QCD, in a time-dependent background, can be written in the general form, $H + O(H^2)$, where $H$ is the Hubble parameter. Based on this, a phenomenological dark energy model whose energy density is of the form $ρ=αH+βH^{2}$ was recently proposed to explain the dark energy dominated universe. In this paper, we investigate this generalized ghost dark energy model in the setup of Brans-Dicke cosmology. We study the cosmological implications of this model. In particular, we obtain the equation of state and the deceleration parame…
