  We analyze non-minimally coupled scalar field theories in metric
(second-order) and Palatini (first-order) formalisms in a comparative fashion.
After contrasting them in a general setup, we specialize to inflation and find
that the two formalisms differ in their predictions for various cosmological
parameters. The main reason is that dependencies on the non-minimal coupling
parameter are different in the two formalisms. For successful inflation, the
Palatini approach prefers a much larger value for the non-minimal coupling
parameter than the Metric approach. Unlike the Metric formalism, in Palatini,
the inflaton stays well below the Planck scale whereby providing a natural
inflationary epoch.
