Constant-roll in the Palatini-$R^2$ models

We consider models of a scalar field coupled to quadratic $R\text{\hspace{0.17em}⁣}+\text{\hspace{0.17em}⁣}{R}^2$ gravity in the framework of the Palatini formulation. The resulting Einstein-frame generalized $k$-inflation effective theory is analyzed assuming that the constant-roll condition holds. We focus on a quartic self-interaction potential, a case of particular appeal modelling Higgs inflation, considering the cases of minimal and non-minimal coupling of the inflaton to gravity. For an appropriate range of the model parameters in the large field domain the obtained values for the inflationary observables are found in agreement with current observations.