$Om$ diagnostic can differentiate between different models of dark energy without the accurate current value of matter density. We apply this geometric diagnostic to dilaton dark energy(DDE) model and differentiate DDE model from LCDM. We also invest
igate the influence of coupled parameter $alpha$ on the evolutive behavior of $Om$ with respect to redshift $z$. According to the numerical result of $Om$, we get the current value of equation of state $omega_{sigma0}$=-0.952 which fits the WMAP5+BAO+SN very well.
Applying the parametrization of dark energy density, we can construct directly independent-model potentials. In Born-Infeld type phantom dark energy model, we consider four special parametrization equation of state parameter. The evolutive behavior o
f dark energy density with respect to red-shift $z$, potentials with respect to $phi$ and $z$ are shown mathematically. Moreover, we investigate the effect of parameter $eta$ upon the evolution of the constructed potential with respect to $z$. These results show that the evolutive behavior of constructed Born-Infeld type dark energy model is quite different from those of the other models.
Statefinder diagnostic is a useful method which can differ one dark energy model from the others. The Statefinder pair ${r, s}$ is algebraically related to the equation of state of dark energy and its first time derivative. We apply in this paper thi
s method to the dilaton dark energy model based on Weyl-Scaled induced gravitational theory. We investigate the effect of the coupling between matter and dilaton when the potential of dilaton field is taken as the Mexican hat form. We find that the evolving trajectory of our model in the $r-s$ diagram is quite different from those of other dark energy models.
Using a new method--statefinder diagnostic which can differ one dark energy model from the others, we investigate in this letter the dynamics of Born-Infeld(B-I) type dark energy model. The evolutive trajectory of B-I type dark energy with Mexican ha
t potential model with respect to $e-folding$ time $N$ is shown in the $r(s)$ diagram. When the parameter of noncanonical kinetic energy term $etato0$ or kinetic energy $dot{phi}^2to0$, B-I type dark energy(K-essence) model reduces to Quintessence model or $Lambda$CDM model corresponding to the statefinder pair ${r, s}$=${1, 0}$ respectively. As a result, the the evolutive trajectory of our model in the $r(s)$ diagram in Mexican hat potential is quite different from those of other dark energy models.
In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as coupled Quintessence, which is called DCQ model by us. Parametrization of the dark energy model is a good method by which we can construct the scalar potential directly f
rom the effective equation of state function $omega_sigma(z)$ describing the properties of the dark energy. Applying this method to the DCQ model, we consider four parametrizations of $omega(z)$ and investigate the features of the constructed DCQ potentials, which possess two different evolutive behaviors called O mode and E mode. Lastly, we comprise the results of the constructed DCQ model with those of quintessence model numerically.
We generally investigate the scalar field model with the lagrangian $L=F(X)-V(phi)$, which we call it {it General Non-Canonical Scalar Field Model}. We find that it is a special square potential(with a negative minimum) that drives the linear field s
olution($phi=phi_0t$) while in K-essence model(with the lagrangian $L=-V(phi)F(X)$) the potential should be taken as an inverse square form. Hence their cosmological evolution are totally different. We further find that this linear field solutions are highly degenerate, and their cosmological evolutions are actually equivalent to the divergent model where its sound speed diverges. We also study the stability of the linear field solution. With a simple form of $F(X)=1-sqrt{1-2X}$ we indicate that our model may be considered as a unified model of dark matter and dark energy. Finally we study the case when the baryotropic index $gamma$ is constant. It shows that, unlike the K-essence, the detailed form of F(X) depends on the potential $V(phi)$. We analyze the stability of this constant $gamma_0$ solution and find that they are stable for $gamma_0leq1$. Finally we simply consider the constant c_s^2 case and get an exact solution for F(X)
In this paper, we investigate the dynamics of Born-Infeld(B-I) phantom model in the $omega-omega$ 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 $omega-omega$ plane, and show mathematically the property of attractor solutions which correspond to $omega_phisim-1$, $Omega_phi=1$, which avoid the Big rip problem and meets the current observations well.
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 $omega-omega$ plane, which is defined by the equation o
f 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 $omega-omega$ plane, and show mathematically the property of attractor solutions which correspond to $omega_sigmasim-1$, $Omega_sigma=1$. Finally, we find that our model is a tracking one which belongs to freezing type model classified in $omega-omega$ plane.
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 corre
spond to an equation of state parameter $omega=-1$ and a cosmic density parameter $Omega_sigma=1$. We find that the coupled term between matter and dilaton cant affect the existence of attractor solutions. In the Mexican hat potential, the attractor behaviors, the evolution of state parameter $omega$ and cosmic density parameter $Omega$, are shown mathematically. Finally, we show the effect of coupling term on the evolution of $X(frac{sigma}{sigma_0})$ and $Y(frac{dot{sigma}}{sigma^2_0})$ with respect to $N(lna)$ numerically.
