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We discuss the evolution of holographic hessence model, which satisfies the holographic principle and can naturally realize the equation of state crossing −1. By discussing the evolution of the models in the w–w′ plane, we find that, if c⩾1, whe⩾−1 and keep for all time, which are quintessence-like. However, if c<−1, which mildly favors the current observations, whe evolves from whe>−1 to whe<−1, and the potential is a nonmonotonic function. In the earlier time, the potential must be rolled down, and then be climbed up. Considered the current constraint on the parameter c, we reconstruct the potential of the holographic hessence model.

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... Although, there isn't a quantum theory of gravity, one can proceed to investigate the nature of dark energy based on some principles of quantum gravity. A tremendous try in this regard is dubbed holographic dark energy (HDE) proposal [11,12]. As a rule, in the quantum field theory, ρ Λ as zero-point energy density is defined based on L (the size of the current universe) as follow ...

... where, according to (12), we using Ω f φ + Ω m φ = 1. Now we must obtain the equation of state parameter for ρ f and corresponding pressure p f , p f = ω f ρ f . ...

We investigate the corresponding relation between f(R) gravity and holographic dark energy. We introduce a type of energy density from f(R) that has the same role as holographic dark energy. We obtain the differential equation that specifies the evolution of the introduced energy density parameter based on a varying gravitational constant. We discover the relation for the equation of state parameter for low redshifts that contains varying G correction.

... Instead of vacuum energy, the quintom field is taken as a holographic dark energy with phantom-crossing behavior. The model is known as hessence model [131]. Taking ability in unifying of inflation and phantom-crossing late time acceleration, a model was invented to accommodate the unifying picture. ...

We consider a cosmological model of non-minimal derivative coupling (NMDC) to gravity with holographic effect from Bekenstein-Hawking entropy using Hubble horizon IR cutoff. Holographic parameter $c$ is constant in a range, $0 \leq c < 1$. NMDC effect allows gravitational constant to be time-varying. Definition of holographic density include time-varying part of the gravitational constant. NMDC part reduces strength of gravitational constant for $\k > 0$ and opposite for $\k < 0$. The holographic part enhances gravitational strength. We use spectral index and tensor-to-scalar ratio to test the model against CMB constraint. Number of e-folding is chosen to be $N \geq 60$. Potentials, $V = V_0 \phi^n $ with $n = 2, 4$, and $V = V_0 \exp{(-\beta \phi)}$ are considered. Combined parametric plots of $\k$ and $\phi$ show that the allowed regions of the power spectrum index and of the tensor-to-scalar ratio are not overlapping. NMDC inflation is ruled out and the holographic NMDC inflation is also ruled out for $0 < c < 1$. NMDC significantly changes major anatomy of the dynamics, i.e. it gives new late-time attractor trajectories in acceleration regions. The holographic part clearly affects pattern of trajectories. However, for the holographic part to affect shape of the acceleration region, the NMDC field must be in presence. To constrain the model at late time, variation of gravitational constant is considered. Gravitational-wave standard sirens and supernovae data give a constraint, $\dot{G}/G|_{t_0} \lesssim 3\times10^{-12} \, \text{year}^{-1}$ \cite{Zhao:2018gwk} which, for this model, results in $ 10^{-12} \, \text{year}^{-1} \, \gtrsim \, {- \kappa} \dot{\phi}\ddot{\phi}/{M^2_{\p}}\,. $ Positive $\k$ is favored and greater $c^2$ results in lifting up lower bound of $\k$.

... Among various scalar field models available, there is unique one called Hessence. It is a non-canonical complex scalar field which plays the role of quintom (i.e., hybrid of quintessence and phantom) [39][40][41][42][43]. The action of the field can be given by, ...

In this work, we have tried to find out similarities between various available models of scalar field dark energies (e.g., quintessence, k-essence, tachyon, phantom, quintom, dilatonic dark energy, etc). We have defined an equivalence relation from elementary set theory between scalar field models of dark energies and used fundamental ideas from linear algebra to set up our model. Consequently, we have obtained mutually disjoint subsets of scalar field dark energies with similar properties and discussed our observation.

... HDE is usually considered to be a very different model of DE compared to scalar field models. However, it is interesting to note that with non-trivial potentials, one can use scalar field to reconstruct HDE Guberina et al. (2005b); Kim et al. (2005);Zhang (2007Zhang ( , 2006; Setare (2007d,a,b); Zhang et al. (2007b);Zhao (2007); Setare and Saridakis (2009);Cruz et al. (2009); Karami and Fehri (2010b); Rozas-Fernandez (2011). ...

We review the paradigm of holographic dark energy (HDE), which arises from a theoretical attempt of applying the holographic principle (HP) to the dark energy (DE) problem. Making use of the HP and the dimensional analysis, we derive the general formula of the energy density of HDE. Then, we describe the properties of HDE model, in which the future event horizon is chosen as the characteristic length scale. We also introduce the theoretical explorations and the observational constraints for this model. Next, in the framework of HDE, we discuss various topics, such as spatial curvature, neutrino, instability of perturbation, time-varying gravitational constant, inflation, black hole and big rip singularity. In addition, from both the theoretical and the observational aspects, we introduce the interacting holographic dark energy scenario, where the interaction between dark matter and HDE is taken into account. Furthermore, we discuss the HDE scenario in various modified gravity (MG) theories, such as Brans-Dicke theory, braneworld theory, scalar-tensor theory, Horava-Lifshitz theory, and so on. Besides, we introduce the attempts of reconstructing various scalar-field DE and MG models from HDE. Moreover, we introduce other DE models inspired by the HP, in which different characteristic length scales are chosen. Finally, we make comparisons among various HP-inspired DE models, by using cosmological observations and diagnostic tools.

... Models of DE include quintessence [13], quintom [14][15][16][17][18], phantom [19], Chaplygin gas [20], tachyon [21], and h-essence [22]. These models can be classified according to the behavior of the equation of state (EoS) parameter, DE , as follows: (i) cosmological constant, in which the EoS parameter is exactly equal to -1, that is, DE = -1; (ii) quintessence, in which the EoS parameter remains above the cosmological constant boundary, that is, DE ≥ -1; (iii) phantom, in which the EoS parameter lies below the cosmological constant boundary, that is, DE ≤ -1; and (iv) quintom, in which the EoS parameter is able to evolve across the cosmological constant boundary. ...

In this paper, we consider a recently proposed model of Dark Energy (DE)
know as Modified Holographic Ricci DE (MHRDE) (which is function of the
Hubble parameter and its first derivative with respect to the cosmic
time $t$) in the light of the $f(R,T)$ model of modified gravity,
considering the particular model $f(R,T) = \mu R + \nu T$, with $\mu$
and $\nu$ constants. The equation of state (EoS) parameter
$\omega_{\Lambda}$ approaches but never reaches the value -1, implying a
quintessence-like behavior of the model. The deceleration parameter $q$
passes from decelerated to accelerated phase at a redshift of $z\approx
0.2$, showing also a small dependence from the values of the parameters
considered. Thanks to the statefinder diagnostic analysis, we observed
that the $\Lambda$CDM phase for the considered model is attainable. We
observed that the fractional energy densities for DE and DM
$\Omega_{\Lambda}$ and $\Omega_m$ have, respectively, an increasing and
a decreasing pattern with the evolution of the universe, indicating an
evolution from matter to DE dominated universe. Finally, studying the
squared speed of the sound $v_s^2$ for our model, we found that is
classically stable.

... Models of DE include quintessence [26], phantom [28], quintom [27], Chaplygin gas [29], tachyon [30], hessence [31] etc. All DE models can be classified by the behaviors of equations of state as following [27]:(i)Cosmological constant: its EoS is exactly equal to −1, that is w DE = −1; ...

In the present work we have considered a modified gravity dubbed as
"logarithmic $f(T)$ gravity" and investigated the behavior of Ricci dark energy
interacting with pressureless dark matter. We have chosen the interaction term
in the form $Q\propto H\delta\rho_{m}$ and investigated the behavior of the
Hubble parameter $H$ as a function of the redshift $z$. For this reconstructed
$H$ we have investigated the behavior of the density of the Ricci dark energy
$\rho_{RDE}$ and density contribution due to torsion $\rho_{T}$. All of the
said cosmological parameters are seen to have increasing behavior from higher
to lower redshifts for all values of $c^{2}$ pertaining to the Ricci dark
energy. Subsequently, we observed the equation of state parameter $w_{RDE}$ in
this situation. The equation of state parameter is found to behave like phantom
for all choices of $c^{2}$ in the Ricci dark energy.

... However, as is well known, it is plagued by the so-called " cosmological constant problem " and " coincidence problem " [2]. Other dark energy models include quintessence [5], phantom [6], quintom [1], Chaplygin gas [7], tachyon [8], hessence [9] etc. All DE models can be classified by the behaviors of equations of state as following [1]: ...

In this paper we have considered an interacting Ricci dark energy in flat Friedman-Robertson-Walker (FRW) universe. We have reconstructed the Hubble parameter under this interaction. Also, we have investigated the statefinder diagnostics. It has been revealed that the equation-of-state parameter behaves like quintessence in this interaction and from the statefinder diagnostics it has been concluded that the interacting Ricci dark energy interpolates between dust and Lambda CDM stages of the universe.

... However, as is well known, it is plagued by the so-called "cosmological constant problem" and "coincidence problem" [2]. Other dark energy models include quintessence [5], phantom [6], quintom [1], Chaplygin gas [7], tachyon [8], hessence [9] etc. ...

In the present work, we have considered N-dimensional Einstein field
equations in which 4-dimensional space-time is described by a FRW metric and
that of the extra d-dimensions by an Euclidean metric. Considering the universe
filled with tachyonic field we have reconstructed the potential $V(\phi)$
corresponding to the field reconstructions in an anisotropic universe under
\emph{Emergent-Power law}, \emph{Emergent-Intermediate},
\emph{Emergent-Logamediate}and \emph{Logamediate-Intermediate} scenarios. The
statefinder parameters have been investigated in all of the said scenarios.

Regenerated silk fibers typically fall short of silkworm cocoon fibers in mechanical properties due to reduced fiber crystal structure and alignment. One approach to address this has been to employ inorganic materials as reinforcing agents. The present study avoids the need for synthetic additives, demonstrating the first use of exfoliated silk nanofibers to control silk solution crystallization, resulting in all-silk pseudocomposite fibers with remarkable mechanical properties. Incorporating only 0.06 wt. % silk nanofibers led to a ∼44% increase in tensile strength (over 600 MPa) and ∼33% increase in toughness (over 200 kJ/kg) compared with fibers without silk nanofibers. These remarkable properties can be attributed to nanofiber crystal seeding in conjunction with fiber draw. The crystallinity nearly doubled from ∼17% for fiber spun from pure silk solution to ∼30% for the silk nanofiber reinforced sample. The latter fiber also shows a high degree of crystal orientation with a Herman's orientation factor of 0.93, a value which approaches that of natural degummed B. mori silk cocoon fiber (0.96). This study provides a strong foundation to guide the development of simple, eco-friendly methods to spin regenerated silk with excellent properties and a hierarchical structure that mimics natural silk.
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Within the framework of quantum gravity and modified entropy-area formalism, the Tsallis holographic dark energy is an effort to peep into a mysterious content of the Universe, the dark energy, to analyze its nature. The Tsallis parameter [Formula: see text] provides the main characteristic of the Tsallis holographic dark energy. Opting the value of Tsallis parameter [Formula: see text], a quintessence scalar field description of the Tsallis holographic dark energy model can be obtained. In this work, we present this quintessential explanation of the Tsallis holographic dark energy with [Formula: see text] and reconstruct the dynamics of the scalar field and the potential of quintessence.

In the present study, we investigate the Bianchi type III cosmological model in the context of Brans–Dicke (BD) theory of gravitation. We assume viscous holographic dark energy as a matter source. Exact solutions of the field equations are obtained. Two different models based on parameter m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m$\end{document} are investigated. It is observed that the viscosity and BD coupling constant have a measurable effect on dynamical quantities. Some physical parameters are also discussed.

Since it was first discovered, thousands of years ago, silkworm silk has been known to be an abundant biopolymer with a vast range of attractive properties. The utilization of silk fibroin (SF), the main protein of silkworm silk, has not been limited to the textile industry but has been further extended to various high-tech application areas, including biomaterials for drug delivery systems and tissue engineering. The outstanding mechanical properties of SF, including its facile processability, superior biocompatibility, controllable biodegradation, and versatile functionalization have allowed its use for innovative applications. In this review, we describe the structure, composition, general properties, and structure-properties relationship of SF. In addition, the methods used for the fabrication and modification of various materials are briefly addressed. Lastly, recent applications of SF-based materials for small molecule drug delivery, biological drug delivery, gene therapy, wound healing, and bone regeneration are reviewed and our perspectives on future development of these favorable materials are also shared.

Geometric sigma model is a purely geometric theory in which spacetime
coordinates are seen as scalar fields coupled to gravity. Although it looks
like ordinary sigma model, it has the peculiarity that its complete matter
content can be gauged away. The remaining geometric theory possesses a vacuum
solution that is predefined in the process of constructing the theory. The fact
that vacuum configuration is specified in advance is another peculiarity of
geometric sigma models. In this paper, I construct geometric sigma models based
on the arbitrarily chosen geometry of the Universe. Whatever geometry is
chosen, the dynamics of its small perturbations is shown to be classically
stable. This way, any desirable metric is made a stable solution of a
particular model. The inflationary Universe and the standard model Universe are
considered as examples of how this is done in practice.

The present thesis has concentrated on the various models of dark energy, their interactions and their consequences on the accelerated expansion of the universe. A detailed literature survey on dark energy models has been presented. The dark energy models considered in the present thesis are tachyonic field, scalar field, phantom field, Chaplygin gas, DBI-essence, hessence, new agegraphic dark energy, and Ricci dark energy. Various issues associated with these models have been discussed along with extensive literature survey. In various cases the associated potentials and fields have been reconstructed and their evolutions with respect to cosmic time, scale factor, and redshift have been discerned through parametric plots. The thermodynamic consequences have also been discussed for some interacting dark energy situations.

We study the statefinder parameters in the Yang–Mills condensate dark energy models, and find that the evolving trajectories of these models are different from those of other dark energy models. We also define two eigenfunctions of the Yang–Mills condensate dark energy models. The values of these eigenfunctions are quite close to zero if the equation of state of the Yang–Mills condensate is not far from -1, which can be used to simply differentiate between the Yang–Mills condensate models and other dark energy models.

We study the interacting agegraphic dark energy (ADE) model in the non-flat universe by means of the statefinder diagnostic and an w–w′ analysis. First, the evolution of EoS parameter (wd) and deceleration parameter (q) are calculated in terms of scale-factor for interacting ADE models in the non-flat universe. The dependency of wd on the ADE model parameters n and α in different spatial curvatures is investigated. We show that the evolution of q is dependent on the type of spatial curvature, besides dependening on parameters n and α. The accelerated expansion takes place sooner in the open universe and latter in the closed universe as compared with the flat universe. Then, we plot the evolutionary trajectories of the interacting ADE models for different values of the parameters n and α, as well as for different contributions of spatial curvature, in the plane of statefinder parameters. In addition to the statefinder, we also investigate the ADE model in the non-flat universe with w–w′ analysis.

We investigate the attractor solution in the coupled Yang–Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation of state of dark energy must evolve from wy > 0 to wy ≤ -1, which is slightly suggested by the observation. At the same time, the total equation of state in the attractor solution is wtot = -1, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.

We try to study the corresponding relation between f(T ) gravity and
holographic dark energy (HDE). A kind of energy density from f(T) is introduced
which has the same role as the HDE density. A f(T ) model according to the the
HDE model is calculated .We find out a torsion scalar T based on the scalar
factor is assumed by (Capoziello,Nojiri et al. 2006). The effective torsion
equation of state, deceleration parameter of the holographic f(T )- gravity
model are calculated

In the 5-year WMAP data analysis, a new parametrization form for dark
energy equation-of-state was used, and it has been shown that the
equation-of-state, w(z), crosses the cosmological-constant boundary w =
-1. Based on this observation, in this paper, we investigate the
reconstruction of quintom dark energy model. As a
single-real-scalarfield model of dark energy, the generalized ghost
condensate model provides us with a successful mechanism for realizing
the quintom-like behavior. Therefore, we reconstruct this scalar-field
quintom dark energy model from the WMAP 5-year observational results. As
a comparison, we also discuss the quintom reconstruction based on other
specific dark energy ansatzs, such as the CPL parametrization and the
holographic dark energy scenarios.

The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called "entropy-corrected holographic dark energy" (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called "entropy-corrected agegraphic dark energy" (ECADE).

We make steps in a new direction by considering fluids with EoS of more general form F(ρ,P)=0. It is thought that there should be interaction between cosmic fluids, but this assumption for this stage carries only phenomenological
character opening a room for different kinds of manipulations. In this paper we will consider a modification of an interaction Q, where we accept that interaction parameter b1 (order of unity) in Q=3Hb1ρ is time dependent and presented as a linear function of Hubble parameter H of the form b0+btH, where b and b0 are constants. We consider two different models including modified Chaplygin gas and polytropic gas which have bulk viscosity. Then, we investigate problem numerically and analyze behavior of different cosmological parameters concerning fluids and behavior of the universe.

In this paper the equation of state formalism for the dark energy models on the brane considered and stability of theory investigated. We consider four different cases of the Little Rip, Asymptotic de Sitter, Asymptotic breakdown, and Big Freeze singularity models and find that the only stable model is Asymptotic de Sitter case. In other cases we get negative value of squared sound speed.

In this paper, we study holographic Ricci dark energy model with non-constant c
2 term in dark energy density formula. We consider FRW metric in flat space-time and calculate density. Also we find scale factor and Hubble expansion parameter.

In this paper we consider holographic dark energy model with interaction in the flat space-time with non-zero cosmological constant. We calculate cosmic scale factor and Hubble expansion parameter by using the time-dependent dark energy density. Then, we obtain phenomenological interaction between holographic dark energy and matter. We fixed our solution by using the observational data.

In this paper, we consider holographic Ricci dark energy model, and by using general relativity equations obtain time-dependent density of the Universe. We show that the resulting density in independent of space curvature.

We consider a self-consistent system of Bianchi Type VI0 cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation
of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding
Einstein’s field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in
detail.

In this article we consider the holographic dark energy density. We study dark energy density in Universe with arbitrary spatially
curvature described by the Friedmann-Robertson-Walker metric. We use Jassal-Bagla-Padmanabhan parametrization to specify dark
energy density.

This work is a comprehensive investigation of the Yang–Mills condensate (YMC) dark energy (DE) model, which is extended to include the three-loop quantum corrections. We study its cosmic evolution and the possibility of crossing the phantom divide w = −1, examine in detail the Hubble parameter H, the deceleration parameter q, the statefinder (r,s) diagnostic and the w−w' diagnostic for the model without and with interaction, and compare our results with other DE models. Also, using the observational data for type Ia supernovae (SNIa), the shift parameter from the cosmic microwave background (CMB), and the baryon acoustic oscillation peak from large scale structures (LSS), we give the cosmological constraints on the three-loop YMC model. It is found that the model can solve the coincidence problem naturally, and its prediction of the aforementioned parameter is much closer to the ΛCDM (CDM: cold dark matter) model one than those from other dynamical DE models; the introduction of the matter–DE interaction will make the YMC model deviate from the ΛCDM model, and will give an equation of state crossing −1. Moreover, it is also found that, for fitting the latest SNIa data alone, the ΛCDM model is slightly better than the three-loop YMC model; but in fitting the combination of SNIa, CMB and LSS data, the three-loop YMC model performs better than the ΛCDM model.

In this paper we consider a correspondence between the interacting new agegraphic dark energy density and tachyon energy density
in non-flat universe. Then we reconstruct the potential and the dynamics of the tachyon field which describe tachyon cosmology.

In this article we consider holographic dark energy model with interaction and space curvature. We calculate cosmic scale
factor by using the time-dependent dark energy density. Then we obtain phenomenological interaction between holographic dark
energy and matter.
KeywordsDark energy–Holographic–Cosmology

We investigate the interacting NADE model in non-flat universe. The effects of spatial curvature Ωk
, interaction coefficient α and the main parameter of NADE, n, on EoS parameter w
d
and deceleration parameter q are studied. We obtain a minimum value for n in both early and present time, in order to that our DE model crosses the phantom divide. Also in a closed universe, changing the sign of q is strongly dependent on α. It has been shown that the quantities w
d
and q have a different treatment for various spatial curvature. At last, we calculate the statefinder diagnostic and w−w
′ analysis in non flat universe. In non flat universe, the statefinder trajectories are discriminated by both n and α.

In this article we consider the cosmological model based on the holographic dark energy. We study dark energy density in Universe
with arbitrary spatially curvature described by the Friedmann-Robertson-Walker metric. We use Chevallier-Polarski-Linder parametrization
to specify dark energy density.
KeywordsDark energy–Cosmological constant–Holography

In this paper, we study a cosmological application of the new agegraphic dark energy density in the f(R) gravity framework. We employ the new agegraphic model of dark energy to obtain the equation of state for the new agegraphic
energy density in a spatially flat universe. Our calculations show, taking n<0, that it is possible to have w
Λ crossing −1. This implies that one can generate a phantom-like equation of state from a new agegraphic dark energy model
in a flat universe in the modified gravity cosmology framework. Also, we develop a reconstruction scheme for the modified
gravity with f(R) action.

We explore the late-time dynamics of a four-dimensional homogeneous and isotropic universe based on a modified Brans-Dicke
scalar tensor theory in the presence of string corrections and Gauss-Bonnet curvature corrections. Many original and attractive
cosmological features are revealed and discussed in some details.
KeywordsModified Brans-Dicke cosmology-String corrections-Gauss-Bonnet invariant term-Accelerated expansion

In this article we investigate the relation between the temperature and density of the dark energy. We find that the temperature
of the dark universe is proportional to the inverse of dark energy density. Also we discuss some values of the important parameters
of the theory.
KeywordsDark energy–Cosmological constant–Thermodynamics

We consider a self-consistent system of Plane symmetric cosmology and binary mixture of perfect fluid and dark energy. The
perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding
Einstein’s field equations are obtained as a quadrature. The cases of Zeldovich Universe, Dust Universe and Radiation Universe
and models with power-law and exponential expansion have discussed in detail. For larget, the models tend to be isotropic.
KeywordsCosmological models–Perfect fluid–Dark energy–Cosmological parameters

We investigate canonical, phantom and quintom models, with the various fields being non-minimally coupled to gravity, in the framework of holographic dark energy. We classify them and we discuss their cosmological implications. In particular, we examine the present value of the dark energy equation-of-state parameter and the crossing through the phantom divide, and we extract the conditions for a future cosmological singularity. The combined scenarios are in agreement with observations and reveal interesting cosmological behaviors.

We investigate the restrictions on the equation-of-state parameter of phantom cosmology. due to the minimum quantum gravitational requirements. We find that for all the examined w(Lambda)(z)-parametrizations and for arbitrary phantom potentials and spatial curvature. the phantom equation-of-state parameter is not restricted at all. This is in radical contrast with the quintessence paradigm, and makes phantom cosmology more robust and capable of constituting the underlying mechanism for dark energy.

In this Letter we implement the new agegraphic dark energy model with quintessence field. We demonstrate that the new agegraphic evolution of the universe can be described completely by a single quintessence field. Its potential as a function of the quintessence field is reconstructed numerically. In particular, the analytical solution of the new agegraphic quintessence dark energy model (NAQDE) is approximately obtained in the matter-dominated epoch. Furthermore, we investigate the evolution of the NAQDE model in the ω–ω′ phase plane. It turns out that by quantum corrections, the trajectory of this model lies outside the thawing and freezing regions at early times. But at late times, it enters the freezing regions and gradually approaches to a static cosmological constant state in the future. Therefore the NAQDE should belong to the freezing model at late times. For comparison, we further extend this model by including the interaction between the NADE and DM and discuss its evolution in the ω–ω′ phase plane.

A new dark energy model, named as “agegraphic dark energy”, has been proposed by one of us (R.G. Cai) in [R.G. Cai, arXiv: 0707.4049], based on the Károlyházy uncertainty relation, which arises from the quantum mechanics together with general relativity. Then, in [H. Wei, R.G. Cai, arXiv: 0707.4052], it has been extended by including the interaction between the agegraphic dark energy and the pressureless (dark) matter. In this note, we investigate the agegraphic dark energy models without and with interaction by means of statefinder diagnostic and w–w′ analysis.

In this Letter a connection between the holographic dark energy model and the f(R) theory is established. We treat the f(R) theory as an effective description for the holographic dark energy and reconstruct the function f(R) with the parameter c>1, c=1 and c<1, respectively. We show the distinctive behavior of each cases realized in f(R) theory, especially for the future evolution.

In the holographic Ricci dark energy (RDE) model, the parameter α plays an important role in determining the evolutionary behavior of the dark energy. When α<1/2, the RDE will exhibit a quintom feature, i.e., the equation of state of dark energy will evolve across the cosmological constant boundary w=−1. Observations show that the parameter α is indeed smaller than 1/2, so the late-time evolution of RDE will be really like a phantom energy. Therefore, it seems that the big rip is inevitable in this model. On the other hand, the big rip is actually inconsistent with the theoretical framework of the holographic model of dark energy. To avoid the big rip, we appeal to the extra dimension physics. In this Letter, we investigate the cosmological evolution of the RDE in the braneworld cosmology. It is of interest to find that for the far future evolution of RDE in a Randall–Sundrum braneworld, there is an attractor solution where the steady state (de Sitter) finale occurs, in stead of the big rip.

In this Letter, we investigate the possible theoretical constraint on the parameter n of the agegraphic quintessence model by considering the requirement of the weak gravity conjecture that the variation of the quintessence scalar field ϕ should be less than the Planck mass Mp. We obtain the theoretical upper bound n≲2.5 that is inconsistent with the current observational constraint result 2.637<n<2.983 (95.4% CL). The possible implications of the tension between observational and theoretical constraint results are discussed.

The interacting polytropic gas dark energy model is investigated from the
viewpoint of statefinder diagnostic tool and $w-w^{\prime}$ analysis. The
dependency of the statefinder parameters on the parameter of the model as well
as the interaction parameter between dark matter and dark energy is calculated.
We show that different values of the parameters of model and different values
of interaction parameter result different evolutionary trajectories in $s-r$
and $w-w^{\prime}$ planes. The polytropic gas model of dark energy mimics the
standard $\Lambda$CDM model at the early time.

The present work considers interaction between DBI-essence and other candidates of dark energies like modified Chaplygin gas, hessence, tachyonic field, and new agegraphic dark energy. The potentials of the fields have been reconstructed under interaction and their evolutions have been viewed against cosmic time $t$ and scalar field $\phi$. Equation of state parameters have also been obtained. The nature of potentials and the equation of state parameters of the dark energies have been found graphically in presence of interaction (both small and large interaction). Comment: 13 pages, 18 figures

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SISSA hosts a very high-ranking, large and multidisciplinary scientific research output. The scientific papers produced by its researchers are published in high impact factor, well-known international journals, and in many cases in the world's most prestigious scientific journals such as Nature and Science. Over 900 students have so far started their careers in the field of mathematics, physics and neuroscience research at SISSA.
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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 which try to explain this remarkable crossing behavior. First we show the key observations which imply the crossing behavior. And then we concentrate on the theoretical progresses on the dark energy models which can realize the crossing -1 phenomenon. We discuss three kinds of dark energy models: 1. two-field models (quintom-like), 2. interacting models (dark energy interacts with dark matter), and 3. the models in frame of modified gravity theory (concentrating on brane world). Comment: 42 pages, 17 figs, invited review for Nova Science Publisher, as a chapter of the book Dark Energy: Theories, Developments and Implications

We suggest a correspondence between interacting agegraphic dark energy models and the quintessence scalar field in a non-flat universe. We demonstrate that the agegraphic evolution of the universe can be described completely by a single quintessence scalar field. Then, we reconstruct the potential of the interacting agegraphic quintessence dark energy as well as the dynamics of the scalar field according to the evolution of the agegraphic dark energy. Comment: 12 pages, 12 figures

In this paper we consider the new agegraphic model of interacting dark energy
in non-flat universe. We show that the interacting agegraphic dark energy can
be described by a phantom scalar field. Then we show this phantomic description
of the agegraphic dark energy and reconstruct the potential of the phantom
scalar field.

Motivated by our recent work \cite{set1}, we generalize this work to the interacting non-flat case. Therefore in this paper we deal with canonical, phantom and quintom models, with the various fields being non-minimally coupled to gravity, within the framework of interacting holographic dark energy. We employ the holographic model of interacting dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named $L$. Comment: 18 pages, 3 figures. Accepted for publication in IJMPD (2010)

Bekenstein has proposed the bound S{le}{pi}M{sup 2}{sub P}L{sup 2} on the total entropy S in a volume L{sup 3} . This nonextensive scaling suggests that quantum field theory breaks down in large volume. To reconcile this breakdown with the success of local quantum field theory in describing observed particle phenomenology, we propose a relationship between UV and IR cutoffs such that an effective field theory should be a good description of nature. We discuss implications for the cosmological constant problem. We find a limitation on the accuracy which can be achieved by conventional effective field theory. {copyright} {ital 1999} {ital The American Physical Society}

Important observables to reveal the nature of dark energy are the equation of state w and its time derivative in units of the Hubble time w'. Recently, it was shown that the simplest scalar field models of dark energy (quintessence) occupy rather narrow regions in the w-w(') plane. We extend the w-w' plane to w <-1 and derive bounds on w' as a function of w for tracker phantom dark energy. We also derive bounds on tracker k-essence. The observational window for w' for w <-1 is not narrow, sigma(w') less than or similar to 6 vertical bar 1+w vertical bar.

We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 ≤ z ≤ 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters: the Hubble constant (H0), the mass density (ΩM), the cosmological constant (i.e., the vacuum energy density, ΩΛ), the deceleration parameter (q0), and the dynamical age of the universe (t0). The distances of the high-redshift SNe Ia are, on average, 10%–15% farther than expected in a low mass density (ΩM = 0.2) universe without a cosmological constant. Different light curve fitting methods, SN Ia subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant (i.e., ΩΛ > 0) and a current acceleration of the expansion (i.e., q0 < 0). With no prior constraint on mass density other than ΩM ≥ 0, the spectroscopically confirmed SNe Ia are statistically consistent with q0 < 0 at the 2.8 σ and 3.9 σ confidence levels, and with ΩΛ > 0 at the 3.0 σ and 4.0 σ confidence levels, for two different fitting methods, respectively. Fixing a "minimal" mass density, ΩM = 0.2, results in the weakest detection, ΩΛ > 0 at the 3.0 σ confidence level from one of the two methods. For a flat universe prior (ΩM + ΩΛ = 1), the spectroscopically confirmed SNe Ia require ΩΛ > 0 at 7 σ and 9 σ formal statistical significance for the two different fitting methods. A universe closed by ordinary matter (i.e., ΩM = 1) is formally ruled out at the 7 σ to 8 σ confidence level for the two different fitting methods. We estimate the dynamical age of the universe to be 14.2 ± 1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely effect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these effects appear to reconcile the data with ΩΛ = 0 and q0 ≥ 0.

We measure the large-scale real-space power spectrum PðkÞ by using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z % 0:1. We employ a matrix-based method using pseudo–Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 22 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0:02 h Mpc À1 < k < 0:3 h Mpc À1 . We pay par-ticular attention to modeling, quantifying, and correcting for potential systematic errors, nonlinear redshift distortions, and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum PðkÞ up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0:1 h Mpc À1 , thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the Wilkinson Microwave Anisotropy Probe satellite. The power spectrum is not well-characterized by a single power law but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fitted by a flat scale-invariant adiabatic cosmological model with h m ¼ 0:213 AE 0:023 and 8 ¼ 0:89 AE 0:02 for L Ã galaxies, when fixing the baryon fraction b = m ¼ 0:17 and the Hubble parameter h ¼ 0:72; cosmological interpretation is given in a companion paper.

Using the recently obtained holographic cosmic duality, we reached a reasonable quantitative agreement between predictions of the cosmic microwave background radiation at small l and the WMAP observations, showing the power of the holographic idea. We also got constraints on the dark energy and its behaviour as a function of the redshift upon relating it to the small l CMB spectrum. For a redshift independent dark energy, our constraint is consistent with the supernova results, which again shows the correctness of the cosmic duality prescription. We have also extended our study to the redshift dependence of the dark energy.

Using the low limit of cosmic ages from globular cluster and the white dwarfs: , together with recent new high redshift supernova observations from the HST/GOODS program and previous supernova data, we give a considerable estimation of the equation of state for dark energy, with uniform priors as weak as 0.2<Ωm<0.4 or 0.1<Ωmh2<0.16. We find cosmic age limit plays a significant role in lowering the upper bound on the variation amplitude of dark energy equation of state. We propose in this Letter a new scenario of dark energy dubbed quintom, which gives rise to the equation of state larger than −1 in the past and less than −1 today, satisfying current observations. In addition we have also considered the implications of recent X-ray gas mass fraction data on dark energy, which favors a negative running of the equation of state.

We use the Chandra measurements of the X-ray gas mass fraction of 26 rich clusters released by Allen et al. to perform constraints on the holographic dark energy model. The constraints are consistent with those from other cosmological tests, especially with the results of a joint analysis of supernovae, cosmic microwave background, and large scale structure data. From this test, the holographic dark energy also tends to behave as a quintom-type dark energy. (c) 2005 Elsevier B.V All rights reserved.

A model for holographic dark energy is proposed, following the idea that the short distance cut-off is related to the infrared cut-off. We assume that the infrared cut-off relevant to the dark energy is the size of the event horizon. With the input Omega(Lambda) = 0.73, we predict the equation of state of the dark energy at the present time be characterized by w = -0.90. The cosmic coincidence problem can be resolved by inflation in our scenario, provided we assume the minimal number of e-foldings.

We explore the consequences that follow if the dark energy is phantom energy, in which the sum of the pressure and energy density is negative. The positive phantom-energy density becomes infinite in finite time, overcoming all other forms of matter, such that the gravitational repulsion rapidly brings our brief epoch of cosmic structure to a close. The phantom energy rips apart the Milky Way, solar system, Earth, and ultimately the molecules, atoms, nuclei, and nucleons of which we are composed, before the death of the Universe in a "big rip."

We present evidence that the simplest particle-physics scalar-field models of dynamical dark energy can be separated into distinct behaviors based on the acceleration or deceleration of the field as it evolves down its potential towards a zero minimum. We show that these models occupy narrow regions in the phase plane of w and w', the dark energy equation of state and its time derivative in units of the Hubble time. Restricting an energy scale of the dark energy microphysics limits how closely a scalar field can resemble a cosmological constant. These results, indicating a desired measurement resolution of order sigma(w') approximately = (1+w), define firm targets for observational tests of the physics of dark energy.

We present here the final results of the Hubble Space Telescope Key Project
to measure the Hubble constant. We summarize our method, the results and the
uncertainties, tabulate our revised distances, and give the implications of
these results for cosmology. The analysis presented here benefits from a number
of recent improvements and refinements, including (1) a larger LMC Cepheid
sample to define the fiducial period-luminosity (PL) relations, (2) a more
recent HST Wide Field and Planetary Camera 2 (WFPC2) photometric calibration,
(3) a correction for Cepheid metallicity, and (4) a correction for
incompleteness bias in the observed Cepheid PL samples. New, revised distances
are given for the 18 spiral galaxies for which Cepheids have been discovered as
part of the Key Project, as well as for 13 additional galaxies with published
Cepheid data. The new calibration results in a Cepheid distance to NGC 4258 in
better agreement with the maser distance to this galaxy. Based on these revised
Cepheid distances, we find values (in km/sec/Mpc) of H0 = 71 +/- 2 (random) +/-
6 (systematic) (type Ia supernovae), 71 +/- 2 +/- 7 (Tully-Fisher relation), 70
+/- 5 +/- 6 (surface brightness fluctuations), 72 +/- 9 +/- 7 (type II
supernovae), and 82 +/- 6 +/- 9 (fundamental plane). We combine these results
for the different methods with 3 different weighting schemes, and find good
agreement and consistency with H0 = 72 +/- 8. Finally, we compare these results
with other, global methods for measuring the Hubble constant.

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First the hessence field has finite value in these solutions and second, their stabilities depend on the second derivative of the hessence potential.

Recently a lot of attention has been drawn to build dark energy model in which the equation-of-state parameter $w$ can cross the phantom divide $w=-1$. One of models to realize crossing the phantom divide is called quintom model, in which two real scalar fields appears, one is a normal scalar field and the other is a phantom-type scalar field. In this paper we propose a non-canonical complex scalar field as the dark energy, which we dub ``hessence'', to implement crossing the phantom divide, in a similar sense as the quintom dark energy model. In the hessence model, the dark energy is described by a single field with an internal degree of freedom rather than two independent real scalar fields. However, the hessence is different from an ordinary complex scalar field, we show that the hessence can avoid the difficulty of the Q-balls formation which gives trouble to the spintessence model (An ordinary complex scalar field acts as the dark energy). Furthermore, we find that, by choosing a proper potential, the hessence could correspond to a Chaplygin gas at late times.

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.

Models of dark energy are conveniently characterized by the equation-of-state
parameter w=p/\rho, where \rho is the energy density and p is the pressure.
Imposing the Dominant Energy Condition, which guarantees stability of the
theory, implies that w \geq -1. Nevertheless, it is conceivable that a
well-defined model could (perhaps temporarily) have w<-1, and indeed such
models have been proposed. We study the stability of dynamical models
exhibiting w<-1 by virtue of a negative kinetic term. Although naively
unstable, we explore the possibility that these models might be
phenomenologically viable if thought of as effective field theories valid only
up to a certain momentum cutoff. Under our most optimistic assumptions, we
argue that the instability timescale can be greater than the age of the
universe, but only if the cutoff is at or below 100 MeV. We conclude that it is
difficult, although not necessarily impossible, to construct viable models of
dark energy with w<-1; observers should keep an open mind, but the burden is on
theorists to demonstrate that any proposed new models are not ruled out by
rapid vacuum decay.

We derive a condition for converging a common evolutionary track for k-essence (a scalar field dark energy with non-canonical kinetic terms). For the Lagrangian density V(phi)W(X) with X=dot{phi}^2/2, we find tracker solutions with w_{phi} < w_B exist if Gamma equivalent V''V/(V')^2 > 3/2. Here w_{phi}(w_B) is the equation-of-state of the scalar field (background radiation/matter). Our condition may be useful for examining the existence of the attractor-like behavior in cosmology with k-essence. Comment: 7 pages, minor changes, to appear in Phys.Rev.D

We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72 h^{-3} Gpc^3 over 3816 square degrees and 0.16<z<0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100h^{-1} Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z=1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z=0.35 and z=1089 to 4% fractional accuracy and the absolute distance to z=0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density Omega_mh^2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find Omega_m = 0.273 +- 0.025 + 0.123 (1+w_0) + 0.137 Omega_K. Including the CMB acoustic scale, we find that the spatial curvature is Omega_K=-0.010+-0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental properties.

We examine the possibility that a significant component of the energy density of the universe has an equation-of-state different from that of matter, radiation or cosmological constant ($\Lambda$). An example is a cosmic scalar field evolving in a potential, but our treatment is more general. Including this component alters cosmic evolution in a way that fits current observations well. Unlike $\Lambda$, it evolves dynamically and develops fluctuations, leaving a distinctive imprint on the microwave background anisotropy and mass power spectrum. Comment: revised version, with added references, to appear in Phys. Rev. Lett. (4 pages Latex, 2 postscript figures)

We calculate the angular scale of the acoustic oscillation from the BOOMERANG and WMAP data on the cosmic microwave background (CMB) to constrain the holographic dark energy model recently proposed by Li. We find that only the phantom-like holographic dark energy survives the cosmological tests. This is, however, inconsistent with the positive energy condition implicitly assumed in constructing Li's model. Therefore the model is marginally ruled out by the present CMB data. As a supplementary check, we also calculate the suppression of the matter density fluctuation due to the late time integrated Sach-Wolfe effect by the holographic dark energy, the result is within the tolerance of the cosmic variance. Some aspect about the saturation of the cosmic holographic bound is also discussed. Comment: 13 pages, 4 figures;v2 point out the conflict between energy condition and cmb constraint;v3 add references, redo ISW part

Dark energy rapidly evolving from the dustlike state in the close past to the phantomlike state at present has been recently proposed as the best fit for the supernovae Ia data. Assuming that a dark energy component with an arbitrary scalar-field Lagrangian, which has a general dependence on the field itself and its first derivatives, dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states with w>-1 to those with w<-1 or vice versa. We have found that generally such transitions are physically implausible because they are either realized by a discrete set of trajectories in the phase space or are unstable with respect to the cosmological perturbations. This conclusion is confirmed by a comparison of the analytic results with numerical solutions obtained for simple models. Without the assumption of the dark energy domination, this result still holds for a certain class of dark energy Lagrangians, in particular, for Lagrangians quadratic in field's first derivatives. The result is insensitive to topology of the Friedmann universe as well.

In this paper, we use the type Ia supernova data to constrain the model of holographic dark energy. For $d=1$, the best fit result is $\Omega^0_m = 0.25$, the equation of the state of the holographic dark energy $w^0_\d = -0.91$ and the transition between the decelerating expansion and the accelerating expansion happened when the cosmological red-shift was $z_T=0.72$. If we set $d$ as a free parameter, the best fit results are $d=0.21$, $\Omega_m^0=0.46$, $w_\d^0=-2.67$, which sounds like a phantom today, and the transition redshift is $z_T=0.28$. Comment: 7 pages, 2 figures, harvmac; likelihood of $w^0_\Lambda$ added; v3: a reference corrected; Significant additions on setting d as a free parameter and some references added

The coincidence problem is studied in the effective Yang-Mills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matter-dominated into the dark energy dominated stage only recently $z\sim 0. 3$, and evolve to the present state with $\Omega_{y}\sim 0.73$ and $\Omega_m\sim 0.27$.

Type Ia supernova (SN Ia), galaxy clustering, and cosmic microwave background anisotropy (CMB) data provide complementary constraints on the nature of the dark energy in the universe. We find that the three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations give a CMB shift parameter of R = (\Omega_m H_0^2)^{1/2} \int_0^{z_{CMB}} dz'/H(z')= 1.70 \pm 0.03. Using this new measured value of the CMB shift parameter, together with the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS), and SN Ia data from the HST/GOODS program and the first year Supernova Legacy Survey, we derive model-independent constraints on the dark energy density rho_X(z) and the cosmic expansion rate H(z). We also derive constraints on the dark energy equation of state w_X(z)=w_0+w'z (with cutoff at z=2) and w_X(a)=w_0+(1-a)w_a. We find that current data provide slightly tighter constraints on rho_X(z) and H(z) as free functions in redshift, and roughly a factor of two improvement in constraining w_X(z). A cosmological constant remains consistent with data, however, uncertainties remain large for model-independent constraints of dark energy. Significant increase in the number of observed SNe Ia between redshifts of 1 and 2, complemented by improved BAO and weak lensing cosmography measurements (as expected from the JEDI mission concept for the Joint Dark Energy Mission), will be required to dramatically tighten model-independent dark energy constraints. Comment: 9 pages, including 5 color figures. Substantially revised and expanded version; ApJ in press

Recently, a novel class of models for inflation has been found in which the inflationary dynamics is driven solely by (non-canonical) kinetic terms rather than by potential terms. As an obvious extension, we show that a scalar field with non-canonical kinetic terms alone behaves like an energy component which is time-varying and has negative pressure presently, i.e. quintessence. We present a model which has a constant equation of state, that is, a ``kinetic'' counterpart of the Ratra-Peebles model of a quintessence field with a potential term. We make clear the structure of the phase plane and show that the quintessential solution is a late-time attractor. We also give a model for the ``phantom'' component which has an equation of state with $w=p/\rho <-1$.

In this paper, we study the possibility of building two-field models of dark energy with equation of state across -1. Specifically we will consider two classes of models: one consists of two scalar fields (quintessence + phantom) and another includes one scalar (phantom) and one spinor field (neutrino). Our studies indicate to some extent that two-field models give rise to a simple realization of the dynamical dark energy model with the equation of state across w=-1.

In this paper, we study the holographic dark energy model proposed by Li from the statefinder viewpoint. We plot the evolutionary trajectories of the model with c = 1 in the statefinder parameter-planes. The statefinder diagrams characterize the properties of the holographic dark energy and show the discrimination between this scenario and other dark energy models. We also perform a statefinder diagnostic to the holographic dark energy model in cases of different c which given by three fits to observational data. The result indicates that from the statefinder viewpoint c plays a significant role in this model and should thus be determined seriously by future high precision experiments.

Recently, many efforts have been made to build dark energy models whose equation-of-state parameter can cross the so-called phantom divide wde=-1. One of them is the so-called hessence dark energy model in which the role of dark energy is played by a noncanonical complex scalar field. In this work, we develop a simple method based on Hubble parameter H(z) to reconstruct the hessence dark energy. As examples, we use two familiar parametrizations for H(z) and fit them to the latest 182 type Ia supernovae Gold dataset. In the reconstruction, measurement errors are fully considered.

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field ϕ1 and a phantom field ϕ2, and the potential function has the form of V(ϕ12-ϕ22). This kind of quintom field can be separated into two kinds: the hessence model, which has the state of ϕ12>ϕ22, and the hantom model with the state ϕ12<ϕ22. We discuss the evolution of these models in the ω-ω′ plane (ω is the state equation of the dark energy, and ω′ is its time derivative in units of Hubble time), and find that according to ω>-1 or <-1, and the potential of the quintom being climbed up or rolled down, the ω-ω′ plane can be divided into four parts. The late time attractor solution, if existing, is always quintessencelike or Λ-like for hessence field, so the big rip does not exist. But for hantom field, its late time attractor solution can be phantomlike or Λ-like, and sometimes, the big rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the ω-ω′ plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation-of-state function ω(z). We apply our method to five kinds of parametrizations of equation-of-state parameter, where ω crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom δQ and the metric Φ are all finite even at the state of ω=-1 and ω′≠0.

We investigate in this Letter the cosmological evolution of a dark energy model with two scalar fields where one of the scalar has canonical kinetic energy and another scalar has negative kinetic energy term. For such a system with exponential potentials we find that during the evolution of the universe the equation of state w changes from w⩾−1 to w<−1, which is consistent with the recent observations. A phase-plane analysis shows that the “phantom”-dominated scaling solution is the stable late-time attractor of this type of models.

Entropy bounds render quantum corrections to the cosmological constant Λ finite. Under certain assumptions, the natural value of Λ is of order the observed dark energy density ∼10−10 eV4, thereby resolving the cosmological constant problem. We note that the dark energy equation of state in these scenarios is w≡p/ρ=0 over cosmological distances, and is strongly disfavored by observational data. Alternatively, Λ in these scenarios might account for the diffuse dark matter component of the cosmological energy density.

We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at large distances the potential is that of a 5D theory. We discuss some phenomenological issues in this framework.

It is extraordinary that a number of observations indicate that we live in a spatially flat, low matter density Universe, which is currently undergoing a period of accelerating expansion. The effort to explain this current state has focused attention on cosmological models in which the dominant component of the cosmic energy density has negative pressure, with an equation of state w⩾−1. Remarking that most observations are consistent with models right up to the w=−1 or cosmological constant (Λ) limit, it is natural to ask what lies on the other side, at w<−1. In this regard, we construct a toy model of a “phantom” energy component which possesses an equation of state w<−1. Such a component is found to be compatible with most classical tests of cosmology based on current data, including the recent type 1a SNe data as well as the cosmic microwave background anisotropy and mass power spectrum. If the future observations continue to allow w<−1, then barring unanticipated systematic effects, the dominant component of the cosmic energy density may be stranger than anything expected.

It is shown that a large class of higher-order (i.e. non-quadratic) scalar kinetic terms can, without the help of potential terms, drive an inflationary evolution starting from rather generic initial conditions. In many models, this kinetically driven inflation (or “k-inflation” for short) rolls slowly from a high-curvature initial phase, down to a low-curvature phase and can exit inflation to end up being radiation-dominated, in a naturally graceful manner. We hope that this novel inflation mechanism might be useful in suggesting new ways of reconciling the string dilaton with inflation.

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a nontrivial minimum. For theories with dilatation anomaly one needs as a nontrivial “cosmon condition” that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short distance renormalization group behaviour of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.

The cosmological consequences of a pervasive, rolling, self-interacting, homogeneous scalar field are investigated. A number of models in which the energy density of the scalar field red-shifts in a specific manner are studied. In these models the current epoch is chosen to be scalar-field dominated to agree with dynamical estimates of the density parameter, ..cap omega../sub dyn/approx.0.2, and zero spatial curvature. The required scalar-field potential is ''nonlinear'' and decreases in magnitude as the value of the scalar field increases. A special solution of the field equations which is an attractive, time-dependent, fixed point is presented. These models are consistent with the classical tests of gravitation theory. The Eoetvoes-Dicke measurements strongly constrain the coupling of the scalar field to light (nongravitational) fields. Nucleosynthesis proceeds as in the standard hot big-bang model. In linear perturbation theory the behavior of baryonic perturbations, in the baryon-dominated epoch, do not differ significantly from the canonical scenario, while the presence of a substantial amount of homogeneous scalar-field energy density at low red-shifts inhibits the growth of perturbations in the baryonic fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, either in the radiation-dominated, matter-dominated, or scalar-field-dominated epochs. On the basis of this effect, we argue that these models could reconcile the low dynamical estimates of the mean mass density with the negligibly small spatial curvature preferred by inflation.

We investigate a possible connection between the suppression of the power at low multipoles in the cosmic microwave background (CMB) spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5.

We recently introduced the concept of "k-essence" as a dynamical solution for explaining naturally why the universe has entered an epoch of accelerated expansion at a late stage of its evolution. The solution avoids fine-tuning of parameters and anthropic arguments. Instead, k-essence is based on the idea of a dynamical attractor solution which causes it to act as a cosmological constant only at the onset of matter-domination. Consequently, k-essence overtakes the matter density and induces cosmic acceleration at about the present epoch. In this paper, we present the basic theory of k-essence and dynamical attractors based on evolving scalar fields with non-linear kinetic energy terms in the action. We present guidelines for constructing concrete examples and show that there are two classes of solutions, one in which cosmic acceleration continues forever and one in which the acceleration has finite duration. Comment: 14 pages, 11 figures

We generalize the mechanism proposed in [hep-th/0005016] and show that a four-dimensional relativistic tensor theory of gravitation can be obtained on a delta-function brane in flat infinite-volume extra space. In particular, we demonstrate that the induced Ricci scalar gives rise to Einstein's gravity on a delta-function type brane if the number of space-time dimensions is bigger than five. The bulk space exhibits the phenomenon of infrared transparency. That is to say, the bulk can be probed by gravitons with vanishing four-dimensional momentum square, while it is unaccessible to higher modes. This provides an attractive framework for solving the cosmological constant problem. Comment: 26 pages, 1 ps fig.; v2: references and comments added; v3: minor corrections, matches Phys. Rev. D version

In this paper we study the possibility of building models of dark energy with equation of state across -1 and propose explicitly a model with a single scalar field which gives rise to an equation of state larger than -1 in the past and less than -1 at the present time, consistent with the current observations. Comment: 4 pages, 1 figure, the version accepted by JCAP, presentation improved and references added

The coincidence problem is studied for the dark energy model of effective Yang-Mills condensate in a flat expanding universe during the matter-dominated stage. The YMC energy $\rho_y(t)$ is taken to represent the dark energy, which is coupled either with the matter, or with both the matter and the radiation components. The effective YM Lagrangian is completely determined by quantum field theory up to 1-loop order. It is found that under very generic initial conditions and for a variety of forms of coupling, the existence of the scaling solution during the early stages and the subsequent exit from the scaling regime are inevitable. The transition to the accelerating stage always occurs around a redshift $z\simeq (0.3\sim 0.5)$. Moreover, when the Yang-Mills condensate transfers energy into matter or into both matter and radiation, the equation of state $w_y$ of the Yang-Mills condensate can cross over -1 around $z\sim 2$, and takes on a current value $\simeq -1.1$. This is consistent with the recent preliminary observations on supernovae Ia. Therefore, the coincidence problem can be naturally solved in the effective YMC dark energy models.

We report on a revision of our previous computation of the renormalized expectation value of the stress-energy tensor of a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. This model is important because it demonstrates that quantum effects can lead to violations of the weak energy condition on cosmological scales - on average, not just in fluctuations - although the effect in this particular model is far too small to be observed. The revision consists of modifying the propagator so that dimensional regularization can be used when the dimension of the renormalized theory is not four. Although the finite part of the stress-energy tensor does not change (in D=4) from our previous result, the counterterms do. We also speculate that a certain, finite and separately conserved part of the stress tensor can be subsumed into a natural correction of the initial state from free Bunch-Davies vacuum. Comment: 9 pages, references added

When taking the holographic principle into account, the vacuum energy will acquire dynamical property that its equation of state is evolving. The current available observational data imply that the holographic vacuum energy behaves as quintom-type dark energy. We adopt the viewpoint of that the scalar field models of dark energy are effective theories of an underlying theory of dark energy. If we regard the scalar field model as an effective description of such a holographic vacuum theory, we should be capable of using the scalar field model to mimic the evolving behavior of the dynamical vacuum energy and reconstructing this scalar field model according to the fits of the observational dataset. We find the generalized ghost condensate model is a good choice for depicting the holographic vacuum energy since it can easily realize the quintom behavior. We thus reconstruct the function $h(\phi)$ of the generalized ghost condensate model using the best-fit results of the observational data.

We combine the Ly-alpha forest power spectrum (LYA) from the Sloan Digital Sky Survey (SDSS) and high resolution spectra with cosmic microwave background (CMB) including three-year WMAP, and supernovae (SN) and galaxy clustering constraints to derive new constraints on cosmological parameters. The existing LYA power spectrum analysis is supplemented by constraints on the mean flux decrement derived using a principle component analysis for quasar continua, which improves the LYA constraints on the linear power. We find some tension between the WMAP3 and LYA power spectrum amplitudes, at the similar to 2s level, which is partially alleviated by the inclusion of other observations: we find sigma(8) = 0.85 +/- 0.02 compared to sigma(8) = 0.80 +/- 0.03 without LYA. For the slope, we find n(s) = 0.965 +/- 0.012. We. nd no evidence for the running of the spectral index in the combined analysis, dn/d ln k = -(1.5 +/- 1.2) x 10(-2), in agreement with inflation. The limits on the sum of neutrino masses are significantly improved: Sigma m(v) < 0.17 eV at 95% (< 0.32 eV at 99.9%). This result, when combined with atmospheric and solar neutrino mixing constraints, requires that the neutrino masses cannot be degenerate, m(3)/m(1) > 1.3 (95% c. l.). Assuming a thermalized fourth neutrino, we. nd m(s) 0.26 eV at 95% c. l. and such a neutrino cannot be an explanation for the LSND results. In

The holographic dark energy model is proposed by Li as an attempt for probing the nature of dark energy within the framework of quantum gravity. The main characteristic of holographic dark energy is governed by a numerical parameter $c$ in the model. The parameter $c$ can only be determined by observations. Thus, in order to characterize the evolving feature of dark energy and to predict the fate of the universe, it is of extraordinary importance to constrain the parameter $c$ by using the currently available observational data. In this paper, we derive constraints on the holographic dark energy model from the latest observational data including the gold sample of 182 Type Ia supernovae (SNIa), the shift parameter of the cosmic microwave background (CMB) given by the three-year {\it Wilkinson Microwave Anisotropy Probe} ({\it WMAP}) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). The joint analysis gives the fit results in 1-$\sigma$: $c=0.91^{+0.26}_{-0.18}$ and $\Omega_{\rm m0}=0.29\pm 0.03$. That is to say, though the possibility of $c<1$ is more favored, the possibility of $c>1$ can not be excluded in one-sigma error range, which is somewhat different from the result derived from previous investigations using earlier data. So, according to the new data, the evidence for the quintom feature in the holographic dark energy model is not as strong as before.

We consider the angular power spectrum in a finite universe with different boundary conditions and perform a fit to the CMB, LSS and supernova data. A finite universe could be the consequence of a holographic constraint, giving rise to an effective IR cutoff at the future event horizon. In such a model there is a cosmic duality relating the dark energy equation of state and the power spectrum, which shows a suppression and oscillatory behaviour that is found to describe the low l features extremely well. However, much of the discussion here will also apply if we actually live inside an expanding bubble that describes our universe. The best fit to the CMB and LSS data turns out to be better than in the standard Lambda-CDM model, but when combined with the supernova data, the holographic model becomes disfavored. We speculate on the possible implications. Comment: 16 pages, 5 figures, to appear in JCAP

Recent type Ia supernovae data seem to favor a dark energy model whose equation of state $w(z)$ crosses -1, which is a much more amazing problem than the acceleration of the universe. Either the case that $w(z)$ evolves from above -1 to below -1 or the case that $w(z)$ runs from below -1 to above -1, is consistent with present data. In this paper we show that it is possible to realize the crossing behaviours of both of the two cases by only a single scalar field in frame of Dvali-Gabadadze-Porrati braneworld. At the same time we prove that there does not exist scaling solution in a universe with dust.

In this paper, we investigate the quintessence models with an oscillating equation of state (EoS) and their potentials. From the constructed potentials, which have the EoS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find they are all the oscillating functions of the field $\phi$, and the oscillating amplitudes are decreasing (or increasing) with $\phi$. From the evolutive equation of the field $\phi$, we find this is caused by the expansion of the universe. This also makes that it is very difficult to build a model whose EoS oscillates forever. However one can build a model with EoS oscillating for a period. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $\phi$. We find they all follow the oscillating EoS. Comment: 15 pages, 7 figures, minor typos corrected

We construct the non-canonical kinetic term of a k-essence field directly
from the effective equation of state function $w_k(z)$, which describes the
properties of the dark energy. Adopting the usual parametrizations of equation
of state we numerically reproduce the shape of the non-canonical kinetic term
and discuss some features of the constructed form of k-essence.

In this paper, we study the possibility of building Yang-Mills(YM) field dark energy models with equation of state (EoS) crossing -1, and find that it can not be realized by the single YM field models, no matter what kind of lagrangian or initial condition. But the states of $-1<\omega<0$ and $\omega<-1$ all can be naturally got in this kind of models. The former is like a quintessence field, and the latter is like a phantom field. This makes that one can build a model with two YM fields, in which one with the initial state of $-1<\omega<0$, and the other with $\omega<-1$. We give an example model of this kind, and find that its EoS is larger than -1 in the past and less than -1 at the present time. We also find that this change must be from $\omega>-1$ to $<-1$, and it will go to the critical state of $\omega=-1$ with the expansion of the Universe, which character is same with the single YM field models, and the Big Rip is naturally avoided. Comment: 20 pages, 4 figures. minor typos corrected

We examine the behavior of dark energy models in the plane defined by w (the equation of state parameter for the dark energy) and w' (the derivative of w with respect to the logarithm of the scale factor). For non-phantom barotropic fluids with positive squared sound speed, we find that w' < 3w(w+1), the opposite of the bound on quintessence models previously derived by Caldwell and Linder. Thus, these barotropic models and quintessence models for the dark energy occupy disjoint regions in the w - w' plane. We also derive two new bounds for quintessence models in the w - w' plane: the first is a general bound for any scalar field with a monotonic potential, while the second improves on the Caldwell-Linder bound for tracker quintessence models. Observationally distinguishing barotropic models from quintessence models requires \sigma(w') < 1+w. Comment: 5 pages, 3 figures, references and discussion added, to appear in Phys. Rev. D