We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $ψ$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(ψ, ψ')$. We formulate simple conditions on the value of coupling constant $ξ$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.
Effective equation of state for dark energy: mimicking quintessence and phantom energy through a variable Lambda
虽然在实验宇宙学的各个方面都有越来越多的证据表明宇宙中存在着不消失的暗能量成分，但我们离理解它的最终性质还很远。一个基本的宇宙学常数，λ，是最自然的候选者，但许多动力学机制，以产生一个有效的λ已被设计出来，假设存在一个特殊的标量场（所谓的精华，及其推广）。这些模型本质上是特设的，但它们导致了具有非平凡状态方程（EOS）的时间演化暗能量的吸引人的可能性。大多数，如果不是全部，未来的精密宇宙学实验研究（例如SNAP和普朗克项目）非常仔细地解决了EOS参数化“a la quintessence”的确定。在这里，我们表明，通过将宇宙学数据拟合到这种状态方程，也可以解释为一个基本的，但随时间演化的宇宙学项的暗示：λ = λ（t）。我们通过研究与λ的重整化群（RG）模型相关的有效状态方程来验证这种可能性。我们发现有效EOS可以对应于正常本质和幻影暗能量，具体取决于RG模型单个参数的值。我们的结论是，背后的一个非平凡的状态方程的一个所谓的精髓或幻影标量场实际上可以有一个运行的宇宙学项的基本量子场论。
Motivated by the mathematic theory of split-complex numbers (or hyperbolic numbers, also perplex numbers) and the split-quaternion numbers (or coquaternion numbers), we define the notion of split-complex scalar field and the split-quaternion scalar field. Then we explore the cosmic evolution of these scalar fields in the background of spatially flat Friedmann-Robertson-Walker Universe. We find that both the quintessence field and the phantom field could naturally emerge in these scalar fields. Introducing the metric of field space, these theories fall into a subclass of the multi-field theorie…
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…
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…
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 give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, λ)$ to observable related variables $(w_ϕ, Ω_ϕ, λ)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintesse…
We discuss the possibility of quintessence in the dilatonic domain walls including the Randall-Sundrum brane world. We obtain the zero mode effective action for gravitating objects in the dilatonic domain wall. First we consider the four dimensional (4D) gravity and the Brans-Dicke graviscalar with a potential. This can be further rewritten as a minimally coupled scalar with the Liouville-type potential in the Einstein frame. However this model fails to induce the quintessence on the dilatonic domain wall because the potential is negative. Second we consider the 4D gravity with the dilaton. In…
We perform a detailed analysis of the asymptotic behavior of a multifield cosmological model with phantom terms. Specifically, we consider the Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term, while one scalar field has negative kinetic energy, that is, it has phantom properties. We show that the Hubble function can change sign, and we study the global evolution of the field equation in the finite and infinity regions with the use of Poincaré variables. We find that in the Chiral-Phantom model the limit of the quintessence scalar field is recovered while the cosmo…
Phantom-like behaviour in dilatonic brane-world scenario with induced gravity
Dvali，Gabadadze and Porrati（DGP）模型有一个自加速解，即正分支，其中膜是渐近的de Sitter。德西特时空可以被看作是类精粹行为和类幻影行为之间的边界。我们表明，在一个5D的电子体，其中的电子子有一个指数的潜力，与膜上的诱导引力项，其物质含量只对应于真空能量，正分支的解决方案经历了一个幻影般的阶段，它面临着一个曲率奇点在其无限的未来。奇点可以被解释为“大撕裂”奇点推向无限的未来宇宙时间。膜上的类似幻影的行为发生时并不违反零能量条件。还有另一个解，负分支，在那里膜可以经历一个早期（瞬时）的暴胀阶段由介子场诱导。
We consider a scalar-tensor model of dark energy with Gauss-Bonnet and non-minimal couplings. Exact cosmological solutions were found in absence of potential, that give equations of state of dark energy consistent with current observational constraints, but with different asymptotic behaviors depending on the couplings of the model. A detailed reconstruction procedure is given for the scalar potential and the Gauss-Bonnet coupling for any given cosmological scenario. Particularly, we consider conditions for the existence of a variety of cosmological solutions with accelerated expansion, includ…
We perform a dynamical system analysis of Myrzakulov or F(R, T) gravity, which is a subclass of affinely connected metric theories, where ones uses a specific but non-special connection, which allows for non-zero curvature and torsion simultaneously. We consider two classes of models, we extract the critical points, and we examine their stability properties alongside their physical features. In the Class 1 models, which possess ΛCDM cosmology as a limit, we find the sequence of matter and dark energy eras, and we show that the Universe will result in a dark-energy dominated critical point for …
Some phantom cosmological models without big rip singularity have been constructed in a simple extended theory of gravity. In the geometrical part of the action, a minimally coupled linear function of the Ricci Scalar and the trace of the energy momentum tensor have been considered in place of the Ricci scalar. Four Little Rip and Pseudo Rip models have been investigated where the equation of state parameter evolves asymptotically and sufficiently rapidly to $-1$. The effect of the coupling constant of the extended gravity theory on the dynamics has been discussed. Possible wormhole solutions …
We perform a full investigation on dynamics of a new dark energy model in which the four-derivative of a non-canonical scalar field (tachyon) is non-minimally coupled to the vector torsion. Our analysis is done in the framework of teleparallel equivalent of general relativity which is based on torsion instead of curvature. We show that in our model there exists a late-time scaling attractor (point $P_{4}$), corresponding to an accelerating universe with the property that dark energy and dark matter densities are of the same order. Such a point can help to alleviate the cosmological coincidence…
