Cosmology of a covariant Galileon field

Abstract

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantom-like behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the Lambda-CDM model.

Figures (3)

• Figure 1: The viable parameter space in the $(\alpha, \beta)$ plane for the branch $r_2>0$. We also show several conditions that determine the border between the allowed and excluded regions.
• Figure 2: Evolution of $w_{\rm eff}$ and $w_{\rm DE}$ for the cases: (A) $\alpha=-1.4$, $\beta=-0.8$, $x_{\rm dS}=1$ with initial conditions $r_1=1$, $r_2=10^{-60}$, $\Omega_r=0.99999$ at the redshift $z=3.11 \times 10^8$, (B) $\alpha=0.1$, $\beta=0.049$, $x_{\rm dS}=1$ with initial conditions $r_1=5 \times 10^{-11}$, $r_2=8 \times 10^{-12}$, $\Omega_r=0.999995$ at $z=6.44 \times 10^8$, and (B$'$) the same $\alpha$, $\beta$, $x_{\rm dS}$ as in the case (B) but with different initial conditions $r_1=5 \times 10^{-7}$, $r_2=8 \times 10^{-16}$, $\Omega_r=0.9995$ at $z=6.72 \times 10^6$.
• Figure 3: Evolution of $c_S^2$ and $c_T^2$ for the cases (A) and (B) as in Fig. \ref{['fig2']}.