Scalar field descriptions of two dark energy models

We give a scalar field description of two dark energy parametrizations, and we analyze in detail its cosmology both at the level of background evolution and at the level of linear perturbations. In particular, we compute the statefinder parameters and the growth index as functions of the redshift for both dark energy parametrizations, and the comparison with the $\mathrm{\Lambda }\mathrm{CDM}$ model as well as with a few well-known geometrical dark energy models is shown. In addition, the combination parameter $A=f{\sigma }_8$ of both models is compared against current data.

Figure 1

Equation of state parameter versus redshift for models I and II. The red curve corresponds to model I, while the blue curve corresponds to model II.

Figure 2

Scalar potential (in units of $H_0^2{m}_{pl}^2$) as a function of the canonical scalar field (in units of Planck mass) for models I and II. The red curve corresponds to model I, while the blue curve corresponds to model II. We have assumed that the present value of the scalar field is $\varphi (z=0)=0.5m_{pl}$.

Figure 3

The first statefinder parameter $r$ versus redshift for models I and II. The red curve corresponds to model I, while the blue curve corresponds to model II.

Figure 4

The second statefinder parameter $s$ versus redshift for models I and II. The red curve corresponds to model I, while the blue curve corresponds to model II.

Figure 5

Growth index $\gamma$ versus redshift for model I and for three different scales, $k=2\times {10}^{-3}\mathrm{h}{\mathrm{Mpc}}^{-1}$ (red), $k=4\times {10}^{-3}\mathrm{h}{\mathrm{Mpc}}^{-1}$ (blue), $k=6\times {10}^{-3}\mathrm{h}{\mathrm{Mpc}}^{-1}$ (magenta). The dotted line corresponds to the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 6

The function $f$ versus redshift for model I and for the three different scales considered in Fig. 5. The dotted curve corresponds to the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 7

Same as Fig. 5 but for model II.

Figure 8

Same as Fig. 6 but for model II.

Figure 9

Growth index $\gamma$ versus redshift for models I (red) and II (blue) for scale $k=0.005\mathrm{h}{\mathrm{Mpc}}^{-1}$, for the DGP model [49] (dashed), and two modified gravity models (black for [50] and gray for [51]).

Figure 10

Comparison between observational data (the error bars are shown too) and the prediction of the models I and II for $A(z)={\sigma }_8(z)f(z)$ versus redshift. The red curve corresponds to model I, while the blue curve corresponds to model II.