Inflation with R _(αβ) terms in the Palatini formulation

We study inflation with the most general non-degenerate gravitational action that depends on symmetric part of Ricci tensor coupled to a scalar field in Palatini formulation gravity. use redefinitions shift effect terms from gravity field, and apply result slow-roll inflation. As examples, we consider actions quadratic cubic tensor. In case results are similar $R+\alpha R^2$ has been studied earlier: tensor-to-scalar ratio $r$ can be suppressed by an arbitrary amount, while spectrum is unaffected. case, at factor $2/9$, change spectral index $n_s$ large.