Cosmology of a Covariant Galileon Field

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 phantomlike behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the cold dark matter model with a cosmological constant.

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 $w_{\mathrm{eff}}$ and $w_{\mathrm{DE}}$ for cases: ($A$) $\alpha =-1.4$, $\beta =-0.8$, $x_{\mathrm{dS}}=1$ with initial conditions $r_1=1$, $r_2={10}^{-60}$, ${\Omega }_r=0.99999$ at the redshift $z=3.11\times {10}^8$; ($B$) $\alpha =0.1$, $\beta =0.049$, $x_{\mathrm{dS}}=1$ 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 ($B^{\prime }$) the same $\alpha$, $\beta$, $x_{\mathrm{dS}}$ as in 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 cases ($A$) and ($B$) as in Fig. 2.