PALATINI FORMULATION FOR GAUGE THEORY: IMPLICATIONS FOR SLOW-ROLL INFLATION

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