  We provide the correspondence between the variables in the Jordan frame and
those in the Einstein frame in scalar-tensor gravity and consider the
frame-(in)dependence of the cosmological observables. In particular, we show
that the cosmological observables/relations (redshift, luminosity distance,
temperature anisotropies) are frame-independent. We also study the
frame-dependence of curvature perturbations and find that the curvature
perturbations are conformal invariant if the perturbation is adiabatic and the
entropy perturbation between matter and the Brans-Dicke scalar is vanishing.
The relation among various definitions of curvature perturbations in the both
frames is also discussed, and the condition for the equivalence is clarified.
