Inflation with R2 term in the Palatini formulation

We study scalar field inflation in F(R) gravity in the Palatini formulation of general relativity. Unlike in the metric formulation, in the Palatini formulation F(R) gravity does not introduce new degrees of freedom. However, it changes the relations between existing degrees of freedom, including the inflaton and spacetime curvature. Considering the case F(R) = R + alpha R-2, we find that the R-2 term decreases the height of the effective inflaton potential. By adjusting the value of a, this mechanism can be used to suppress the tensor-to-scalar ratio r without limit in any scalar field model of inflation without affecting the spectrum of scalar perturbations.