Palatini formulation for gauge theory: implications for slow-roll inflation

We consider a formulation of gauge field theory where the $A_\alpha$ and strength $F_{\alpha\beta}$ are independent variables, as in Palatini gravity. For simplest action, this is known to be equivalent usual formulation. add non-minimal couplings between scalar field, solve for insert it back into action. This leads modified terms. slow-roll inflation show that because modifications sector, adding higher order terms inflaton potential does not spoil its flatness, unlike case. Instead they make effective closer quadratic. The also problem Higgs sensitive