We examine the generation of primordial perturbations during an inflationary epoch in generalized theories of gravity when the equations of motion are derived using the Palatini variational principle. Both $f(R)$ and scalar-tensor theories are considered, and we compare our results with those obtained under the conventional metric formalism. Nonlinear generalizations of the action lead to different theories under the two variational choices, and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result: Inflation driven solely by $f(R)$ modifications does not result in suitable curvature perturbations, while scalar-tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes.

• Received 13 October 2010

DOI:https://doi.org/10.1103/PhysRevD.83.044018