Parametrizing the transition to the phantom epoch with supernovae Ia and standard rulers

The reconstruction of a (non)canonical scalar field Lagrangian from the dark energy equation of state (EOS) parameter is studied, where it is shown that any EOS parametrization can be well reconstructed in terms of scalar fields. Several examples of EOS parameters are studied and the particular scalar field Lagrangian is reconstructed. Then, we propose some new parametrizations that may present a (fast) transition to a phantom dark energy EOS (where $w_{\mathrm{DE}}<-1$), and the scalar field Lagrangian is also reconstructed numerically. Furthermore, the properties of these parametrizations of the dark energy EOS are studied by using supernovae Ia data (HST Cluster Supernova Survey) combined with standard ruler data sets [cosmic microwave background (CMB) and baryon acoustic oscillations (BAO)] and its comparison with the $\mathrm{\Lambda }\mathrm{CDM}$ model is analyzed. Then, the best fit of the models is obtained, which provides some information about whether a phantom transition may be supported by the observations. In this regard, the crossing of the phantom barrier is allowed statistically but the occurrence of a future singularity seems unlikely.

Figure 1

Reconstruction of the kinetic term and the scalar potential for the parametrization $w_1$ (solid line) and $w_2$ (dashed line). Here we have assumed $w_0=-0.05$ and $z_0=12.14$ for the model (20) and $w_0=0.1$ and $z_0=-10$ for the model (21).

Figure 2

Evolution of the Hubble parameter assuming the EOS parametrizations (20) and (21) in comparison with $\mathrm{\Lambda }\mathrm{CDM}$ (blue line). For the first model (left panel), the parameter values are $(w_0,z_0)=\{(0.05,34.28),(0.05,12.14),(-0.05,12.14),(-0.1,34.28)\}$ from the upper to the bottom. For the second model (right panel) the values in the same order are $(w_0,z_0)=\{(0.1,12.14),(0.15,12.14),(0.1,-10),(0.15,-10)\}$.

Figure 3

Evolution of the Hubble parameter for the EOS (20) and (21) in comparison with $\mathrm{\Lambda }\mathrm{CDM}$ (blue line). For the first model (left panel), the parameter values are $(w_0,z_0)=\{(0.05,34.28),(0.05,12.14),(-0.05,12.14),(-0.1,34.28)\}$ from the bottom to the upper. For the second model (right panel) the values in the same order are $(w_0,z_0)=\{(0.1,12.14),(0.15,12.14),(0.1,-10),(0.15,-10)\}$.

Figure 4

Values of $E_0=H(0)/H_0$ as a function of the parameters $w_0$ and $z_0$ for the EOS parameters (20) and (21).

Figure 5

Values of $q_0$ as a function of the parameters $w_0$ and $z_0$ for the parametrizations (20) and (21).

Figure 6

Contour plots for the parameters $w_0$ and $z_0$ for the first (left) and second (right) models taking ${\mathrm{\Omega }}_{0\mathrm{m}}=0.27$.

Figure 7

Contour plots of the parameters $w_0$ and $z_0$ for $w_1$ (left) and $w_2$ (right) models using standard rulers data.

Figure 8

Contour plots for the first model (20) when using Sne Ia data and standard rulers.

Figure 9

Contour plots for the second model (21) when combining Sne Ia data and standard rulers.