Conserved cosmological perturbation in Galileon models
  We prove the existence of a fully nonlinear conserved curvature perturbation
on large scales in Galileon-type scalar field models in two approaches. The
first approach is based on the conservation of energy-momentum tensor of the
Galileon field, which is also the familiar approach in understanding the
conservation in $k$-essence or perfect fluid models. We show that the fluid
corresponding to the Galileon field becomes perfect and barotropic on large
scales, which is responsible to the conservation. The difference from
$k$-essence model is that, besides the energy-momentum conservation, the
Einstein equation must be employed in order to complete the proof of barotropy.
In the second approach, we derive the fully non-perturbative action for the
curvature perturbation $\zeta$ in Galileon model on large scales, and argue
that $\zeta=const$ is indeed an exact solution on large scales. This
conservation of curvature perturbation is important since it relates the later
and the primordial universe.
