  We discuss the approaches by Deffayet et al. (DPSV) and Kobayashi et al.
(KYY) to the analysis of linearized scalar perturbations about a spatially flat
FLRW background in Horndeski theory. We identify additional, potentially
important terms in the DPSV approach. However, these terms vanish upon a
judicious gauge choice. We derive a gauge invariant quadratic action for metric
and Galileon perturbations in $\mathcal{L}_3$ and $\mathcal{L}_3+\mathcal{L}_4$
theories and show that actions obtained in the DPSV and KYY approaches follow
from this gauge invariant action in particular gauges.
