Observational constraints on Galileon cosmology

We study the cosmology of a covariant Galileon field $\varphi$ with five covariant Lagrangians and confront this theory with the most recent cosmological probes: the type Ia supernovae data (Constitution and Union2 sets), cosmic microwave background (WMAP7), and the baryon acoustic oscillations (SDSS7). In the Galileon cosmology with a late-time de Sitter attractor, there is a tracker that attracts solutions with different initial conditions to a common trajectory. Including the cosmic curvature $K$, we place observational constraints on two distinct cases: (i) the tracker, and (ii) the generic solutions to the equations of motion. We find that the tracker solution can be consistent with the individual observational data, but it is disfavored by the combined data analysis. The generic solutions fare quite well when a nonzero curvature parameter ${\Omega }_K^{(0)}$ is taken into account, but the Akaike and Bayesian information criteria show that they are not particularly favored over the $\Lambda \mathrm{CDM}$ model.

Figure 1

The evolution of the dark energy equation of state $w_{\mathrm{DE}}$ versus the redshift $z$ for ${\Omega }_K^{(0)}=-0.1$ (left panel) and ${\Omega }_K^{(0)}=0.1$ (right panel) with $\alpha =0.3$ and $\beta =0.14$. We choose the initial conditions as those given in the caption of Fig. 3 of Ref. 24. The tracker solutions ($r_1=1$) are shown as bold lines. For given ${\Omega }_r(N)$, the curvature density parameter ${\Omega }_K(N)$ is determined according to Eq. (22). The two vertical lines denote the present time ($z=0$) and the epoch at decoupling $z=z_{*}$, while the horizontal lines correspond to the $\Lambda \mathrm{CDM}$ model ($w_{\mathrm{DE}}=-1$).

Figure 2

The evolution of $w_{\mathrm{DE}}$ for $\alpha =0.3$ and $\beta =0.14$ with various values of the cosmic curvature ${\Omega }_K^{(0)}=(-0.25,-0.1,0,0.1,0.25)$. The initial conditions are chosen to be $r_1=1.5\times {10}^{-10}$, $r_2=2.667\times {10}^{-12}$, ${\Omega }_r=0.999992$ at $z=3.63\times {10}^8$ [where $N=-\ln (1+z)$]. The meaning of the two vertical lines and the horizontal line is the same as in Fig. 1.

Figure 3

The $68.3\%(1\sigma )–95.4\%(2\sigma )$ ${\chi }^2$ confidence contours in the $({\Omega }_m^{(0)},{\Omega }_K^{(0)})$ plane for (i) the tracker model and (ii) the $\Lambda \mathrm{CDM}$ model. Both contours correspond to the combination of all three data sets, i.e. Constitution $\mathrm{SN}\mathrm{Ia}+\mathrm{BAO}+\mathrm{CMB}$. The best-fit parameters are found in Table . The difference in ${\chi }^2$ between the two models is $\delta {\chi }^2\sim 22$, which corresponds to $\sim 4.3\sigma$. Hence the tracker model is severely disfavored with respect to the $\Lambda \mathrm{CDM}$ model.

Figure 4

The evolution of the dark energy equation of state $w_{\mathrm{DE}}$ for the tracker solution (34) and the nontracker case of Table  (denoted by an *, i.e. $\alpha =1.862$ and $\beta =0.607$ with the initial conditions given in the text). The meaning of two vertical lines and the horizontal line is the same as in Fig. 1.