Inflation with $R^2$ term in the Palatini formalism
  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 $\alpha$, 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.
