  We study the cosmology of a covariant Galileon field 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 non-zero
curvature parameter is taken into account, but the Akaike and Bayesian
information criteria show that they are not particularly favored over the LCDM
model.
