A component of dark energy has been recently proposed to explain the current acceleration of the Universe. Unless some unknown symmetry in Nature prevents or suppresses it, such a field may interact with the pressureless component of dark matter, giving rise to the so-called models of coupled quintessence. In this paper we propose a new cosmological scenario where radiation and baryons are conserved, while the dark energy component is decaying into cold dark matter (CDM). The dilution of CDM particles, attenuated with respect to the usual $a^{-3}$ scaling due to the interacting process, is characterized by a positive parameter $ε$, whereas the dark energy satisfies the equation of state $p_x=ωρ_x$ ($ω< 0$). We carry out a joint statistical analysis involving recent observations from type Ia supernovae, baryon acoustic oscillation peak, and Cosmic Microwave Background shift parameter to check the observational viability of the coupled quintessence scenario here proposed.
We show that the combination of a fluid with a bulk dissipative pressure and quintessence matter can simultaneously drive an accelerated expansion phase and solve the coincidence problem of our current Universe. We then study some scenarios compatible with the observed cosmic acceleration.
We investigate the simplest quintessence dissipative dark matter attractor cosmology characterized by a constant quintessence baryotropic index and a power--law expansion. We show a class of accelerated coincidence--solving attractor solutions converging to this asymptotic behavior. Despite its simplicity, such a ``superattractor'' regime provides a model of the recent universe that also exhibits an excellent fit to supernovae luminosity observations and no age conflict. Our best fit gives $α=1.71\pm 0.29$ for the power-law exponent. We calculate for this regime the evolution of density and en…
Recent cosmological observations reveal that we are living in a flat accelerated expanding universe. In this work we have investigated the nature of the potential compatible with the power law expansion of the universe in a self interacting Brans Dicke cosmology with a perfect fluid background and have analyzed whether this potential supports the accelerated expansion. It is found that positive power law potential is relevant in this scenario and can drive accelerated expansion for negative Brans Dicke coupling parameter $ω$. The evolution of the density perturbation is also analyzed in this s…
We calculate analytically and numerically the Dyer-Roeder distance in perfect fluid quintessence models and give an accurate fit to the numerical solutions for all the values of the density parameter and the quintessence equation of state. Then we apply our solutions to the estimation of $H_{0}$ from multiple image time delays and find that the inclusion of quintessence modifies sensibly the likelihood distribution of $H_{0}$, generally reducing the best estimate with respect to a pure cosmological constant. Marginalizing over the other parameters ($Ω_{m}$ and the quintessence equation of stat…
We analyze the evolution of energy density fluctuations in cosmological scenarios with a mixture of cold dark matter and quintessence, in which the quintessence field is modeled by a constant equation of state. We obtain analytic expressions for the time evolution of the quintessence perturbations in models with light fields. The fluctuations behave analogously to a driven harmonic oscillator, where the driving term arises from the inhomogeneities in the surrounding cosmological fluid. We demonstrate that the homogeneous solution, determined by the initial conditions, is completely sub-dominan…
If the reported measurements of the time variation of the fine structure constant from observations of distant QSOs are correct, combined with the Oklo limit they would strongly constrain the class of the quintessence potential. If these results prove valid, future satellite experiment (STEP) should measure the induced violation of the weak equivalence principle. Future cosmological observations of nearby $(z \siml 0.5)$ absorption systems would make it clear whether the variation is significant or not.
The different definitions for the equation of state of a non-minimally coupled scalar field that have been introduced in the literature are analyzed. Particular emphasis is made upon those features that could yield to an observable way of distinguishing non-minimally coupled theories from General Relativity, with the same or with alternate potentials. It is found that some earlier claims on that super-quintessence, a stage of super-accelerated expansion of the universe, is possible within realistic non-minimally coupled theories are the result of an arguable definition of the equation of state…
The dynamics of interacting dark energy model in loop quantum cosmology (LQC) is studied in this paper. The dark energy has a constant equation of state $w_x$ and interacts with dark matter through a form $3cH(ρ_x+ρ_m)$. We find for quintessence model ($w_x>-1$) the cosmological evolution in LQC is the same as that in classical Einstein cosmology; whereas for phantom dark energy ($w_x<-1$), although there are the same critical points in LQC and classical Einstein cosmology, loop quantum effect reduces significantly the parameter spacetime ($c, w_x$) required by stability. If parameters $c$ and…
We investigate the influence of an exotic fluid component ("quintessence") on the angular size-redshift relation for distant extragalactic sources. Particular emphasis is given for the redshif $z_{m}$ at which the angular size takes its minimal value. We derive an analytical closed form which determines how $z_m$ depends on the parameter of the equation of state describing the exotic component. The results for a flat model dominated by a "quintessence" are compared in detail with the ones for the standard open model dominated by cold dark matter. Some consequences of systematic evolutionary ef…
Within present constraints on the observed smooth energy and its equation of state parameter, it is important to find out whether the smooth energy is static (cosmological constant) or dynamic (quintessence). The most dynamical quintessence fields observationally allowed are now still fast-rolling and no longer satisfy the tracker approximation if the equation of state parameter varies moderately with cosmic scale. We are optimistic about distinguishing between a cosmological constant and appreciably dynamic quintessence, by measuring average values for the effective equation of state paramete…
Neutrinos interacting with the quintessence field can trigger the accelerated expansion of the Universe. In such models with a growing neutrino mass the homogeneous cosmological solution is often unstable to perturbations. We present static, spherically symmetric solutions of the Einstein equations in the same models. They describe astophysical objects composed of neutrinos, held together by gravity and the attractive force mediated by the quintessence field. We discuss their characteristics as a function of the present neutrino mass. We suggest that these objects are the likely outcome of the…
We investigate the properties of cosmological distances in locally inhomogeneous universes with pressureless matter and dark energy (quintessence), with constant equation of state. We give exact solutions for angular diameter distances in theempty beam approximation. In this hypothesis, the distance-redshift equation is derived fron the multiple lens-plane theory. The case of a flat universe is considered with particular attention. We show how this general scheme makes distances degenerate with respect to w_X and the smoothness parameters, alpha, accounting for the homogeneously distributed fr…
This paper implements the idea of considering the instantonic creation of brane worlds whose five-dimensional bulk contains a negative cosmological constant and a scalar quintessence field with time-dependent equation of state, restricting to the case that the quintessence field couples minimally to Hilbert-Einstein gravity. We construct an Euclidean formalism, both for the four- and five-dimensional cases, singling out a Hamiltonian constraint that depends on the parameter defining the quintessence state equation. Specializing at several particular values of that parameter, we obtain solution…
Inflationary cosmology is developed in the second Randall-Sundrum braneworld scenario, where the accelerated expansion arises through potentials that are too steep to drive inflation in conventional cosmology. A relationship between the scalar and tensor perturbation spectra is derived that is independent of both the inflaton potential and the brane tension. It is found that a single field with an inverse power law potential can act as both the inflaton and the quintessence field for suitable values of the brane tension.
Although quintessence cosmologies seem to explain the amount of cosmological constant today, the required conditions are severe. For example, an extremely slowly varying and light scalar field that rolls toward the vanishing vacuum energy state is needed, which must satisfy the required initial conditions so that the energy density in matter is comparable to the energy density stored in quintessence today. Our first question is whether it is possible to explain why quintessence ``knows'' that the Universe is going toward the vanishing energy state. We show from a new perspective that the conve…
In this paper we investigate the effects that a dynamic dark energy component dominant in the universe at late epochs has on reionization. We follow the evolution of HII regions with the analytic approach of Furlanetto and Oh (2005) in two different universes for which we assume the Peebles and Ratra (2003) and Brax and Martin (2000) quintessence models and we compare our results to the LCDM scenario. We show that, for a fixed ionization efficiency, at the same cosmological epoch the topology of bubbles is dominated by high-mass objects and the characteristic size of the ionized regions is sli…
There is a tension between observed Helium abundance and the prediction of the standard Big Bang Nucleosynthesis. We show that non-minimally quintessence model may help to reduce this tension between theory and observation.
A brief account of the current cosmological observations is given and their implications for QCDM and $Λ$CDM cosmologies are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on $Ω_ϕ$ during cosmic evolution, and develop a realistic approach to the tracking behaviour of quintessence fields. The astrophysical constraints are applied to interpolate the value of the tracking parameter $ε\simeq 0.75$ at the present epoch and also to find the lower and the upper limits for $Λ$ in the accelerating universe. It is shown that the transition from decelerat…
Spatially homogeneous models with a scalar field non-minimally coupled to the space-time curvature or to the ordinary matter content are analysed with respect to late-time asymptotic behaviour, in particular to accelerated expansion and isotropization. It is found that a direct coupling to the curvature leads to asymptotic de Sitter expansion in arbitrary exponential potentials, thus yielding a positive cosmological constant although none is apparent in the potential. This holds true regardless of the steepness of the potential or the smallness of the coupling constant. For matter-coupled scal…
A non--minimally coupled quintessence model is investigated and the conditions for a stationary solution to the coincidence problem are obtained. For a conformally coupled scalar field and dissipative matter, a general solution possessing late acceleration is found. It fits rather well the high redshift supernovae data and gives a good prediction of the age of the Universe. Likewise, the cold dark matter component dominates the cosmological perturbations at late times albeit they decrease with expansion.
In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as a coupled quintessence. Based on this consideration, we investigate the dilaton coupled quintessence(DCQ) model in $ω-ω'$ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to $N$(the logarithm of the scale factor $a$). We find the scalar field equation of motion in $ω-ω'$ plane, and show mathematically the property of attractor solutions which correspond to $ω_σ\sim-1$, $Ω_σ=1$. Finally, we find that our model is a tracking one which belongs to "freezing"…
Scalar-tensor theories are the best motivated alternatives to general relativity and provide a mathematically consistent framework to test the various observable predictions. They can involve three functions of the scalar field: (i) a potential (as in "quintessence" models), (ii) a matter-scalar coupling function (as in "extended quintessence", where it may also be rewritten as a nonminimal coupling of the scalar field to the scalar curvature), and (iii) a coupling function of the scalar field to the Gauss-Bonnet topological invariant. We recall the main experimental constraints on this class …
Fanaroff-Riley type IIb (FR IIb) radio galaxies provide a modified standard yardstick that allows constraints to be placed on global cosmological parameters. A sample of 20 FR IIb radio galaxies with redshifts between 0 and 2 are compared with the parent population of 70 radio galaxies to determine the coordinate distance to each source. The coordinate-distance determinations are used to constrain the current mean mass-energy density of quintessence $Ω_q$, the equation of state of the quintessence w, and the current mean mass-energy density of nonrelativistic matter $Ω_m$; zero space curvature…
Based on dilatonic dark energy model, we consider two cases: dilaton field with positive kinetic energy(coupled quintessence) and with negative kinetic energy(phantom). In the two cases, we investigate the existence of attractor solutions which correspond to an equation of state parameter $ω=-1$ and a cosmic density parameter $Ω_σ=1$. We find that the coupled term between matter and dilaton can't affect the existence of attractor solutions. In the Mexican hat potential, the attractor behaviors, the evolution of state parameter $ω$ and cosmic density parameter $Ω$, are shown mathematically. Fin…
The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study a coupled quintessence scenario in which the scalar field evolves in a power law potential and the mass of dark matter particles depends on a power law function of $ϕ$. It is shown that this scenario has a stable attractor solution and can thus provide a natural solution to the cosmic coincidence problem.
It is shown that a minimally coupled scalara field in Brans-Dicke theory yields a non-decelerated expansion for the present universe for open, flat and closed Friedmann-Robertson-Walker models.
We propose a new quintessence scenario in the brane cosmology, assuming that a quintessence field $Q$ is confined in our 3-dimensional brane world. With a potential $V(Q)= μ^{α+4} Q^{-α}~(α\geq 2)$, we find that the density parameter of the scalar field decreases as $Ω_Q \sim a^{-4(α-2)/(α+2)}$ in the epoch of quadratic energy density dominance, if $α\leq 6$. This attractor solution is followed by the usual tracking quintessence scenario after a conventional Friedmann universe is recovered. With an equipartition of initial energy density, we find a natural and successful quintessence model for…
We consider a model of interacting cosmological constant/quintessence, where dark matter and dark energy behave as, respectively, two coexisting phases of a fluid, a thermally excited Bose component and a condensate, respectively. In a simple phenomenological model for the dark components interaction we find that their energy density evolution is strongly coupled during the universe evolution. This feature provides a possible way out for the coincidence problem affecting many quintessence models.
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid of ordinary matter, together with a self-interacting scalar field fluid accounting for the dark energy in the universe. A priori assumptions about the functional form of the self-interaction potential or about the scale factor behavior are not neccessary. These are obtained as outputs of the assumed linear relationship between the Hubble expansion parameter a…
The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both quintessential fields are studied for the same cosmological model. The systems of evolutionary equations for gauge-invariant perturbations of metrics, matter and quintessence have been analysed analyticaly for the early stage of the Universe life and numerically up to the present epoch. It is shown that amplitudes of the adiabatic matter density perturbations grow like …
We study the cosmological evolution of the universe when quintessence is modeled within supergravity, supersymmetry is broken in a hidden sector, and we also include observable matter in a third independent sector. We find that the presence of hidden sector supersymmetry breaking leads to modifications of the quintessence potential. We focus on the coupling of the SUGRA quintessence model to the MSSM and investigate two possibilities. First one can preserve the form of the SUGRA potential provided the hidden sector dynamics is tuned. The currently available limits on the violations of the equi…
We examine the cosmic microwave background (CMB) anisotropy for signatures of early quintessence dark energy -- a non-negligible quintessence energy density during the recombination and structure formation eras. In contrast to a $Λ$CDM cosmology, early quintessence leads to a larger suppression of structure growth. Because of this influence on the clustering of dark matter and the baryon-photon fluid, we may expect to find trace signals in the CMB and the mass fluctuation power spectrum. In detail, we demonstrate that suppressed clustering power on small length-scales, as suggested by the comb…
In this paper we investigate the cosmological effects of modified gravity with string curvature corrections added to Einstein-Hilbert action in the presence of a dynamically evolving scalar field coupled to Riemann invariants. The scenario exhibits several features of cosmological interest for late universe. It is shown that higher order stringy corrections can lead to a class of dark energy models consistent with recent observations. The model can give rise to quintessence, deSitter or phantom dark energy, in last case without recourse to negative kinetic energy field. The detailed treatment …
The effects of mass-varying neutrinos on cosmic microwave background (CMB) anisotropies and large scale structures (LSS) are studied. In these models, dark energy and neutrinos are coupled such that the neutrino masses are functions of the scalar field playing the role of dark energy. We begin by describing the cosmological background evolution of such a system. It is pointed out that, similar to models with a dark matter/dark energy interaction, the apparent equation of state measured with SNIa can be smaller than -1. We then discuss the effect of mass-varying neutrinos on the CMB anisotropie…
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 revise the stability of the tracking solutions and briefly review the potentials of quintessence models. We discuss the evolution of linear perturbations for $V(ϕ) = V_{0} \exp(λϕ^2/2)$ potential in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. We find that the phenomenology of this model is consistent with current observations up to the coupling power $n_{c} \leq 0.01$ while adopting the current parameters measured by WMAP, $Ω_ϕ^{(0)}=0.76$,…
While there is mounting evidence in all fronts of experimental cosmology for a non-vanishing dark energy component in the Universe, we are still far away from understanding its ultimate nature. A fundamental cosmological constant, Lambda, is the most natural candidate, but many dynamical mechanisms to generate an effective Lambda have been devised which postulate the existence of a peculiar scalar field (so-called quintessence, and generalizations thereof). These models are essentially ad hoc, but they lead to the attractive possibility of a time-evolving dark energy with a non-trivial equatio…
The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study two cases of the coupled quintessence scenario. $(a)$ Assume that the mass of dark matter particles depends exponentially on the scalar field associated to dark energy and meanwhile the scalar field evolves in an exponential potential; $(b)$ Assume that the mass of dark matter particles depends on a power law function of the scalar field and meanwhile the scalar field evolves in a power law potential. Since the dynamics of…
Adiabatic perturbations in the cosmology of a quintessential scalar field with exponential potential gravitationally coupled to radiation/matter are investigated in a gauge invariant formalism. The main question addressed in this paper is if the inhomogenous fluctuations can be ignored as often argued and the result is that this is not always the case. Consequences for microwave background radiation and structure formation in the matter dominated era are considered.
A new component of the cosmic medium, a light scalar field or ''quintessence '', has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant. Such a field is expected to be coupled explicitely to ordinary matter, unless some unknown symmetry prevents it. I investigate the cosmological consequences of such a coupled quintessence (CQ) model, assuming an exponential potential and a linear coupling. This model is conformally equivalent to Brans-Dicke Lagrangians with power-law potential. I evaluate the density perturbations on the cosmic microwave background an…
We discuss the evolution of linear perturbations in a quintessence model in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. Due to the modification of the scale of cold dark matter as $ρ_{c} = ρ_{c}^{(0)} a^{-3 + ξ}$, we can shift the turnover in the matter power spectrum even without changing the present energy densities of matter and radiation. This can be used to constrain the strength of the coupling. We find that the phenomenology of this mod…
We discuss observational consequences of a class of cosmological models characterized by the dilution of pressureless matter attenuated with respect to the usual $a^{-3}$ scaling due to the decay of vacuum energy. We carry out a joint statistical analysis of observational data from the new \emph{gold} sample of 182 SNe Ia, recent estimates of the CMB shift parameter, and BAO measurements from the SDSS to show that such models favor the decay of vacuum only into the dark matter sector, and that the separately conserved baryons cannot be neglected. In order to explore ways to more fundamentally …
The case of a coupling between dark energy and matter (Coupled Quintessence) or gravity (Extended Quintessence) has recently attracted a deep interest and has been widely investigated both in the Einstein and in the Jordan frames (EF, JF), within scalar tensor theories. Focusing on the simplest models proposed so far, in this paper we study the relation existing between the two scenarios, isolating the Weyl scaling which allows to express them in the EF and JF. Moreover, we perform a comparative study of the behavior of linear perturbations in both scenarios, which turn out to behave in a mark…
We consider the evolution of linear perturbations in models with a nonminimal coupling between dark matter and scalar field dark energy. Growth of matter inhomogeneities in two examples of such models proposed in the literature are investigated in detail. Both of these models are based on a low-energy limit of effective string theory action, and have been previously shown to naturally lead to late acceleration of the universe. However, we find that these models can be ruled out by taking properly into account the impact of the scalar field coupling on the formation of structure in the dark mat…
If the cold dark matter consists of weakly interacting massive particles (WIMPs), anticipated measurements of the WIMP properties at the Large Hadron Collider (LHC) and the International Linear Collider (ILC) will provide an unprecedented experimental probe of cosmology at temperatures of order 1 GeV. It is worth emphasizing that the expected outcome of these tests may or may not be consistent with the picture of standard cosmology. For example, in kination-dominated quintessence models of dark energy, the dark matter relic abundance can be significantly enhanced compared to that obtained from…
Imagine a scenario in which the dark energy forms via the condensation of dark matter at some low redshift. The Compton wavelength therefore changes from small to very large at the transition, unlike quintessence or metamorphosis. We study CMB, large scale structure, supernova and radio galaxy constraints on condensation by performing a 4 parameter likelihood analysis over the Hubble constant and the three parameters associated with Q, the condensate field: Omega_Q, w_f and z_t (energy density and equation of state today, and redshift of transition). Condensation roughly interpolates between L…
A light scalar field, minimally or not-minimally coupled to the metric field, is a well-defined candidate for the dark energy, overcoming the coincidence problem intrinsic to the cosmological constant and avoiding the difficulties of parameterizations. We present a general description of the weak gravitational lensing valid for every metric theory of gravity, including vector and tensor perturbations for a non-flat spatial metric. Based on this description, we investigate two minimally-coupled scalar field quintessence models using VIRMOS-Descart and CFHTLS cosmic shear data, and forecast the …
Kination dominated quintessence models of dark energy have the intriguing feature that the relic abundance of thermal cold dark matter can be significantly enhanced compared to the predictions from standard cosmology. Previous treatments of such models do not include a realistic embedding of inflationary initial conditions. We remedy this situation by constructing a viable inflationary model in which the inflaton and quintessence field are the same scalar degree of freedom. Kination domination is achieved after inflation through a strong push or "kick" of the inflaton, and sufficient reheating…
The properties of nearby galaxy clusters limit the range of cosmological parameters consistent with our universe. We describe the limits which arise from studies of the intracluster medium (ICM) mass fraction fICM and consideration of the possible sources of systematic error: Omega_M<0.44h_{50}^{-1/2} at 95% confidence. We emphasize that independent of Type Ia supernovae (SNe Ia) observations, this cluster study, taken together with published cosmic microwave background (CMB) anisotropy studies, indicates a non-zero quintessence or dark energy component Omega_Q>0. We then discuss future galaxy…
Models with dark energy decaying into dark matter have been proposed to solve the coincidence problem in cosmology. We study the effect of such coupling in the matter power spectrum. Due to the interaction, the growth of matter density perturbations during the radiation dominated regime is slower compared to non-interacting models with the same ratio of dark matter to dark energy today. This effect introduces a damping on the power spectrum at small scales proportional to the strength of the interaction and similar to the effect generated by ultrarelativistic neutrinos. The interaction also sh…
We study the change of the effective fine structure constant in the cosmological models of a scalar field with a non-vanishing coupling to the electromagnetic field. Combining cosmological data and terrestrial observations we place empirical constraints on the size of the possible coupling and explore a large class of models that exhibit tracking behavior. The change of the fine structure constant implied by the quasar absorption spectra together with the requirement of tracking behavior impose a lower bound of the size of this coupling. Furthermore, the transition to the quintessence regime i…
Modern ideas in quantum gravity predict the possibility of Lorenz Invariance Violation (LIV) manifested e.g. by energy dependent modification of standard relativistic dispersion relation. In a recent paper Jacob and Piran proposed that time of flight delays in high energy neutrinos emitted by gamma ray bursts (GRBs) located at cosmological distances can become a valuable tool for setting limits on LIV theories. However, current advances in observational cosmology suggest that our Universe is dominated by dark energy with relatively little guidance on its nature thus leading to several cosmolog…
We investigate the impact of quantum fluctuations on a light rolling quintessence field from three different sources, namely, from a coupling to the standard model and dark matter, from its self-couplings and from its coupling to gravity. We derive bounds for time-varying masses from the change of vacuum energy, finding Δm_e/m_e << 10^{-11} for the electron and Δm_p/m_p << 10^{-15} for the proton since redshift z~2, whereas the neutrino masses could change of order one. Mass-varying dark matter is also constrained. Next, the self-interactions are investigated. For inverse power law potentials,…
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-dime…
The value of scalar field coupled to gravity should be less than the Planck scale in the consistent theory of quantum gravity. It provides a theoretic constraint on the equation of state parameter for the quintessence. In some cases our theoretic constraints are more stringent than the constraints from the present experiments.
