We study a flat 3-brane in presence of a linear $k$ field with nonzero cosmological constant $Λ_{4}$. In this model the crossing of the phantom divide (PD) occurs when the $k$-essence energy density becomes negative. We show that in the high energy regime the effective equation of state has a resemblance of a modified Chaplygin gas while in the low energy regime it becomes linear. We find a scale factor that begins from a singularity and evolves to a de Sitter stable stage while other solutions have a super-accelerated regime and end with a big rip. We use the energy conditions to show when the effective equation of state of the brane-universe crosses the PD.
Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings in canonical and minimally coupled scalar field and Possible Solutions in $k$-essence Models
High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；ICREA（加泰罗尼亚高级研究中心）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Khazar University（哈扎尔大学）
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.
In this paper, we propose two new models in $f(T)$ gravity to realize the crossing of the phantom divide line for the effective equation of state, and we then study the observational constraints on the model parameters. The best fit results suggest that the observations favor a crossing of the phantom divide line.
An exact solution describing the evolution of the type Bang-to-Rip with the phantom divide line crossing is constructed in the Chameleon cosmology model, based on two independent functions of the scalar field.
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 …
The role of the interaction in reaching and crossing the phantom divide line in the Chaplygin gas model is discussed. We obtain some necessary properties of the interaction that allow the model to arrive at or cross the phantom divide line. We show that these properties put some conditions on the ratio of dark matter to dark energy density in the present epoch.
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 propose a phantom crossing Dvali--Gabadadze--Porrati (DGP) model. In our model, the effective equation of state of the DGP gravity crosses the phantom divide line. We demonstrate crossing of the phantom divide does not occur within the framework of the original DGP model or the DGP model developed by Dvali and Turner. By extending their model, we construct a model that realizes crossing of the phantom divide. We find that the smaller the value of the new introduced parameter $β$ is, the older epoch crossing of the phantom divide occurs in. Our model can account for late-time acceleration of…
We study a model of $F(R)$ gravity in which a crossing of the phantom divide can be realized. In particular, we demonstrate the behavior of $F(R)$ gravity around a crossing of the phantom divide by taking into account the presence of cold dark matter.
We study the equation of state for dark energy and explicitly demonstrate that the future crossings of the phantom divide line $w_{\mathrm{DE}}=-1$ are the generic feature in the existing viable $f(R)$ gravity models. We also explore the future evolution of the cosmological horizon entropy and illustrate that the cosmological horizon entropy oscillates with time due to the oscillatory behavior of the Hubble parameter. The important cosmological consequence is that in the future, the sign of the time derivative of the Hubble parameter changes from negative to positive in these viable $f(R)$ gra…
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 (…
We construct cosmological models with two scalar fields, which has the structure as in the ghost condensation model or k-essence model. The models can describe the stable phantom crossing, which should be contrasted with one scalar tensor models, where the infinite instability occurs at the crossing the phantom divide. We give a general formulation of the reconstruction in terms of the e-foldings N by including the matter although in the previous two scalar models, which are extensions of the scalar tensor model, it was difficult to give a formulation of the reconstruction when we include matt…
It is known that scalar-tensor theory of gravity admits regular crossing of the phantom divide line $w_{\DE}=-1$ for dark energy, and existing viable models of present dark energy for its particular case -- $f(R)$ gravity -- possess one such crossing in the recent past, after the end of the matter dominated stage. It was recently noted that during the future evolution of these models the dark energy equation of state $w_{\DE}$ may oscillate with an arbitrary number of phantom divide crossings. In this paper we prove that the number of crossings can be infinite, present an analytical condition …
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.
An explicit model of $F(R)$ gravity with realizing a crossing of the phantom divide is reconstructed. In particular, it is shown that the Big Rip singularity may appear in the reconstructed model of $F(R)$ gravity. Such a Big Rip singularity could be avoided by adding $R^2$ term or non-singular viable $F(R)$ theory to the model because phantom behavior becomes transient.
We study a holographic model for the dark energy considered recently in the literature which postulates an energy density $ρ\sim R$, where $R$ is the Ricci scalar curvature. We obtain a cosmological scenario that comes from considering two non-interacting fluids along a reasonable Ansatz for the cosmic coincidence parameter. We adjust the involved parameters in the model according to the observational data and we show that the equation of state for the dark energy experience a cross through the -1 barrier. In addition, we find a disagreement in these parameters with respect to an approach from…
We investigate the oscillating effective equation of state (EoS) of the universe around the phantom divide in the framework of $F(R)$ gravity. We illustrate the behavior of $F(R)$ with realizing multiple crossings of the phantom divide.
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…
We investigate the possibility of crossing a phantom divide line in the extension of symmetric teleparallel gravity or the $f(Q)$ gravity, where $Q$ is the non-metricity. We study the cosmic evolution of the effective equation of state parameter for dark energy considering exponential, logarithmic, and combined $f(Q)$ theories. Moreover, the exponential model behaves like the $Λ$CDM at high redshifts before deviating to $ω_{eff}<-1$ or $ω_{eff}>-1$, respectively, depending on the value of model parameter. It also approaches a de-sitter phase asymptotically. However, the crossing of the phantom…
Recently, type Ia supernovae data appear to support a dark energy whose equation of state $w$ crosses -1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in the gravity with an additional inverse power-law term of Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with $w<-1$ or $w>-1$ are obtained. A minimal coupled scalar with different pot…
In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model with 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 $Λ$CDM one, is characterized by a set of p…
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）
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…
We propose a phantom crossing Dvali--Gabadadze--Porrati (DGP) model. In our model, the effective equation of state of the DGP gravity crosses the phantom divide line. We demonstrate crossing of the phantom divide does not occur within the framework of the original DGP model or the DGP model developed by Dvali and Turner. By extending their model, we construct a model that realizes crossing of the phantom divide. DGP models can account for late-time acceleration of the universe without dark energy. Phantom Crossing DGP model is more compatible with recent observational data from Type Ia Superno…
We study possible crossing of the phantom divide line in a DGP-inspired $F(R,ϕ)$ braneworld scenario where scalar field and curvature quintessence are treated in a unified framework. With some specific form of $F(R,ϕ)$ and by adopting a suitable ansatz, we show that there are appropriate regions of the parameters space which account for late-time acceleration and admit crossing of the phantom divide line.
Conditions needed to cross the phantom divide line in an interacting holographic dark energy model in closed Friedmann- Robertson-Walker universe are discussed. The probable relationship between this crossing and the coincidence problem is studied.
We study possible crossing of the phantom divided barrier in a Lorentz invariance violating dark energy model. Lorentz invariance violation which is achieved by introducing a vector field in the action, incorporates directly in the dynamics of the scalar field and equation of state. This interesting feature allows us to study phantom divided barrier crossing in the context of Lorentz invariance violation. We show that for suitable choice of parameter space, equation of state can cross phantom divided barrier just by one scalar field and Lorentz violating vector field controls this crossing.
We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom…
The $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. We shall explore phantom behavior of $f(R)$ models in this frame and compare the results with those of the usual notion of phantom scalar field.
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 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 consider the Chiral cosmological model consisting of two scalar fields minimally coupled to gravity. In the context of a Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) space-time, and for massless fields in the presence of a cosmological constant, we present the general solution of the field equations. The minisuperspace configuration that possesses maximal symmetry leads to scenarios which - depending on the admissible value of the parameters - correspond to a quintessence, quintom or phantom case. The canonical quantization of the model retrieves this distinction as different families of…
Choosing various natural forms for the equation-of-state parameter w and the bulk viscosity ζ, we discuss how it is possible for a dark energy fluid to slide from the quintessence region across the divide w=-1 into the phantom region, and thus into a Big Rip future singularity. Different analytic forms for ζ, as powers of the scalar expansion, are suggested and compared with experiments.
In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann--Robertson--Lama\^ıtre--Walker universe coupled minimally to two quintom fields: one quintessence and one phantom. We examine a classical cosmological framework, where analytical solutions are obtained. Indeed, we present an explanation of the ``big-bang'' singularity by means of a ``big-bounce''. Moreover, having a barotropic fluid description and f…
We show that, in the context of the two-field measure theory, any k-essence model leads to the existence of a fluid made of non-relativistic matter and cosmological constant that would explain the dark matter and dark energy problem at the same time. On the other hand, kinetic gravity braiding models can lead to different behaviors, such as phantom dark energy, stiff matter, and a cosmological constant. For stiff matter, there even exists the case where the scalar field does not have any effect in the dynamics of the Universe.
We study the observational constraints on the Phantom Crossing DGP model. We demonstrate that the crossing of the phantom divide does not occur within the framework of the original Dvali-Gabadadze-Porrati (DGP) model or the DGP model developed by Dvali and Turner. By extending their model in the framework of an extra dimension scenario, we study a model that realizes crossing of the phantom divide. We investigate the cosmological constraints obtained from the recent observational data of Type Ia Supernovae, Cosmic Microwave Background anisotropies, and Baryon Acoustic Oscillations. The best fi…
Here, DGP model of brane-gravity is analyzed and compared with the standard general relativity and Randall-Sundrum cases using non-linear equation of state. Phantom fluid is known to violate the weak energy condition. In this paper, it is found that this characteristic of phantom energy is affected drastically by the negative brane-tension $λ$ of the RS-II model. It is found that in DGP model strong energy condition(SEC) is always violated and the universe accelerates only where as in RS-II model even SEC is not violated for $1 < ρ/λ< 2$ and the universe decelerates.
We restrict purely kinetic k-essence. Assuming the equation of state is a power law of the kinetic energy: $w=w_0X^α$, to obtain accelerated phases, we must have $α>0$ as one of necessary conditions, constrained from the conditions for stability and causality, and the k-essence must behave like phantom. We also study the evolutions of the equation of state and the speed of sound with numerical simulation.
In this paper we consider FRW cosmology in modified gravity which contain arbitrary functions $f(ϕ)$. It is shown that the bouncing solution appears in the model whereas the equation of state (EoS) parameter crosses the phantom divider. The reconstruction of the model is also investigated with the aim to reconstruct the arbitrary functions and variables of the model.
We consider a Tsallis holographic dark energy model with interaction between dark energy and matter. The density of dark energy is taken as $ρ_d \sim 3C^2/L^{4-2γ}$, where $C$, $γ$ are constants. The event horizon is chosen as the characteristic scale $L$. The cosmological dynamics of the universe are analyzed, with special attention paid to the possibility of crossing the phantom line $w_{eff}=-1$. It is shown that for certain values of parameters this may occur not only once, but also twice.
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 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 consider two alternative dark energy models: a Lorentz invariance preserving model with a nonminimally coupled scalar field and a Lorentz invariance violating model with a minimally coupled scalar field. We study accelerated expansion and dynamics of equation of state parameter in these scenarios. While a minimally coupled scalar field has not the capability to be a successful dark energy candidate with cosmological constant line crossing, a nonminimally coupled scalar field in the presence of Lorentz invariance or a minimally coupled scalar field with Lorentz invariance violation have this…
The holographic principle is applied to a flat Friedmann-Robertson-Walker space-time dominated by dark energy when this is due to the presence of a k-essence scalar field, both for dark energy and phantom scenarios. In this framework, a geometrical covariant approach permits the construction of holographic hypersurfaces. The resulting covariant preferred screens, both for phantom and non-phantom regions, are then compared with those obtained by using the holographic dark energy model with the future event horizon as the infrared cut-off. In the phantom case, one of the two obtained holographic…
We study thermodynamics of the apparent horizon in $F(R)$ gravity. In particular, we demonstrate that a $F(R)$ gravity model with realizing a crossing of the phantom divide can satisfy the second law of thermodynamics in the effective phantom phase as well as non-phantom one.
Charging Across the Phantom Divide with Modified Gravity
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Berkeley Center for Cosmological Physics & Berkeley Lab, University of California, Berkeley（加州大学伯克利分校伯克利宇宙学物理中心与伯克利实验室）
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 …
The cosmic acceleration is one of the most significant cosmological discoveries over the last century. Following the more accurate data a more dramatic result appears: the recent analysis of the observation data (especially from SNe Ia) indicate that the time varying dark energy gives a better fit than a cosmological constant, and in particular, the equation of state parameter $w$ (defined as the ratio of pressure to energy density) crosses -1 at some low redshift region. This crossing behavior is a serious challenge to fundamental physics. In this article, we review a number of approaches whi…
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…
We construct phantom energy models with the equation-of-state parameter $w$ such that $w<-1$, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ("phantom energy" without "Big Rip" singularity) and (ii) energy density tends to constant value with time ("cosmological constant" with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitte…
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 propose a model of dark energy consists of a single scalar field with a general non-minimal kinetic couplings to itself and to the curvature. We study the cosmological dynamics of the equation of state in this setup. The coupling terms have the form $ξ_{1} R f(ϕ)\partial_μϕ\partial^μϕ$ and $ξ_{2} R_{μν}f(ϕ)\partial^μϕ\partial^νϕ$ where $ξ_{1}$ and $ξ_{2}$ are coupling parameters and their dimensions depend on the type of function $f(ϕ)$. We obtain the conditions required for phantom divide crossing and show numerically that a cosmological model with general non-minimal derivative coupling t…
A phantom solution in the framework of the causal Israel-Stewart (IS) formalism is discussed. We assume a late time behavior of the cosmic evolution by considering only one dominant matter fluid with viscosity. In the model it is assumed a bulk viscosity of the form $ξ= ξ_{0}ρ^{1/2}$, where $ρ$ is the energy density of the fluid. We evaluate and discuss the behavior of the thermodynamical parameters associated to this solution, like the temperature, rate of entropy, entropy, relaxation time, effective pressure and effective EoS. A discussion about the assumption of near equilibrium of the form…
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 perform a study both statistical and theoretical for cosmological models of matter creation and their ability to describe effective phantom models of dark energy. Such models are beyond the $Λ$CDM model since the resulting cosmic expansion is not adiabatic. In fact, we show that this approach exhibits transient phantom/quintessence scenarios at present time and tends to the standard cosmological model at some stage of the cosmic evolution. We discuss some generalities of the thermodynamics properties for this type of cosmological model; we emphasize on the behavior of the temperature associ…
