We show explicitly, by using astrophysical data plus reasonable assumptions for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity may be high enough to drive the fluid from its position in the quintessence region at present time $t=0$ across the barrier $w=-1$ into the phantom region in the late universe. The phantom barrier is accordingly not a sharp mathematical divide, but rather a fuzzy concept. We also calculate the limiting forms of various thermodynamical quantities, including the rate of entropy production, for a dark energy fluid near the future Big Rip singularity.
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.
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.
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.
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 review the equation of state for dark energy in modified gravity theories. In particular, we summarize the generic feature of the phantom divide crossing in the past and future in viable $f(R)$ gravity models.
We study the dynamics of a bulk viscosity model in the Eckart approach for a spatially flat Friedmann-Robertson-Walker (FRW) universe. We have included radiation and dark energy, assumed as perfect fluids, and dark matter treated as an imperfect fluid having bulk viscosity. We also introduce an interaction term between the dark matter and dark energy components. Considering that the bulk viscosity is proportional to the dark matter energy density and imposing a complete cosmological dynamics, we find bounds on the bulk viscosity in order to reproduce a matter-dominated era (MDE). This constrai…
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.
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…
We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling `triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We study capability of $f(R)$ gravity models to allow crossing the phantom boundary in both Jordan and Einstein conformal frames. In Einstein frame, these models are equivalent to Einstein gravity together with a scalar field minimally coupled to gravity. This scalar degree of freedom appears as a quintessence field with a coupling with the matter sector. We investigate evolution of the equation of sate parameter for some cosmologically viable $f(R)$ gravity models in both conformal frames. This investigation (beyond mere theoretical arguments) acts as an operational tool to distinguish physic…
In standard cosmology, with the evolution of the universe, the matter density and thermodynamic pressure gradually decreases. Also in course of evolution, the matter in the universe obeys (or violates) some restrictions or energy conditions. If the matter distribution obeys strong energy condition (SEC), the universe is in a decelerating phase while violation of SEC indicates an accelerated expansion of the universe. In the period of accelerated expansion the matter may be either of quintessence nature or of phantom nature depending on the fulfilment of the weak energy condition (WEC) or viola…
We investigate the phase space dynamics of a bulk viscosity model in the Eckart approach for a spatially flat Friedmann-Robertson-Walker universe. We have included two barotropic fluids and a dark energy component. One of the barotropic fluids is treated as an imperfect fluid having bulk viscosity, whereas the other components are assumed to behave as perfect fluids. Both barotropic fluids are identified as either radiation or dark matter. Considering that the bulk viscosity acts on either radiation or dark matter, we find that viscous phantom solutions with stable behavior are not allowed in …
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.
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 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.
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 …
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.…
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 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.
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.
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…
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 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…
Oscillatory dark energy with phantom crossings in Einstein-Gauss-Bonnet gravity
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Department of Physics, Indian Institute of Technology, Kanpur（坎普尔印度理工学院物理系）
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…
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 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…
Phantom-Crossing Dark Energy and the $Ω_m$ Tug-of-War
Princeton University（普林斯顿大学）；Laboratoire univers et particules de Montpellier (LUPM), Centre national de la recherche scientifique (CNRS) et Université de Montpellier（蒙彼利埃大学与法国国家科学研究中心联合宇宙与粒子物理实验室）
The $Λ$CDM model is a remarkably successful model which is consistent with the observations of cosmic microwave background radiation (CMB), baryon acoustic oscillation (BAO), and large scale structure of the Universe. However, the discrepancy in the value of $H_0$ between the local observations and PLANCK observation of CMB was recently pointed out. One of the way to ease the discrepancy is to introduce phantom dark energy instead of the cosmological constant. While, phantom dark energy often suffer from the instabilities. We will investigate the general solution to overcome the difficulty of …
We construct a single scalar field model with tachyon field non-minimally coupled to itself, its derivative and to the curvature. We study the cosmological dynamics of the equation of state in this setup. While it is expected that in the case of single scalar field the crossing of the phantom divide line can not be realized [10], we show that incorporating quantum corrections, namely, non-minimal derivative coupling of scalar field with curvature in our model, lead to phantom divide crossing.
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 study dynamics of the equation of state parameter for a dark energy component non-minimally coupled to induced gravity on a warped DGP brane. We show that there are appropriate domains of the model parameters space that account for crossing of the phantom divide line. This crossing, which is possible for both branches of the scenario, depends explicitly on the values of the non-minimal coupling and warp factor. The effect of warp factor appears in the value of the redshift parameter at which phantom divide line crossing occurs.
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…
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 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…
The phantom dark energy remarkably boosts our prehension of the accelerating Universe. Various models are widely discussed in the phantom Universe without bulk viscosity. From the hydrodynamics' point of view, it is natural to introduce the nonperfect fluid in the study of the Universe, as an ideal fluid just an approximation to the real world after all and using the generalized equation of state (EoS) with bulk viscosity, the early inflationary universe and the accelerated expansion of the late-time universe are described by many authors. In this paper, in order to investigate how the viscosi…
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…
A method for deriving Friedmann-Robertson-Walker (FRW) solutions developed in Int. J. Mod. Phys. D{\bf 5}(1996)71-84, is generalized to account for models with non-minimal coupling between the dark energy and the dark matter. New quintessence and phantom (flat) FRW solutions are found. Their physical significance is discussed. Additionally, the aforementioned method is modified so that, "coincidence free" solutions can be readily derived. Besides, we review some aspects of the phantom barrier crossing. In this regard we present a model which is free from the coincidence problem and, at the sam…
We investigate the cosmic acceleration and the evolution of dark energy across the cosmological constant boundary in universal extra dimensions UED. We adopt an empirical approach to solve the higher-dimensional cosmological equations so that the deceleration parameter $q$ is consistent with observations. The expressions for the jerk and deceleration parameters are independent of the number of dimensions $n$. The behavior of pressure in $4$D shows a positive-to-negative transition corresponding to the deceleration-to-acceleration cosmic transition. This pressure behavior helps in providing an …
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…
National Institute for Theoretical & Computational Science（国家理论与计算科学研究所）；Department of Physics & Astronomy, University of the Western Cape（西开普大学物理与天文学系）
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…
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）；Department of Physics, Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学物理系）；Center for Theoretical Physics, Khazar University（阿塞拜疆汗沙尔大学理论物理中心）
Evolution of a background space-time metric and sub-horizon matter density perturbations in the Universe is numerically analyzed in viable $f(R)$ models of present dark energy and cosmic acceleration. It is found that viable models generically exhibit recent crossing of the phantom boundary $w_{\rm DE}=-1$. Furthermore, it is shown that, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative temporarily.
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 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…
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 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…
No evidence for phantom crossing: local goodness-of-fit improvements do not persist under global Bayesian model comparison
University of the Western Cape（西开普大学）；National Institute for Theoretical & Computational Science（理论与计算科学国家研究所）；Missouri University of Science & Technology（密苏里科技大学）；University of Tokyo（东京大学）
We investigate the cosmological evolution in a universe governed by the extended, varying-mass, nonlinear massive gravity, in which the graviton mass is promoted to a scalar-field. We find that the dynamics, both in flat and open universe, can lead the varying graviton mass to zero at late times, offering a natural explanation for its hugely-constrained observed value. Despite the limit of the scenario towards standard quintessence, at early and intermediate times it gives rise to an effective dark energy sector of a dynamical nature, which can also lie in the phantom regime, from which it alw…
