Inflation from charged scalar and primordial magnetic fields?

A model of inflation is presented where the inflaton field is a complex scalar field coupled to a U(1) gauge field. Because of the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by U(1). Because of the coupling of the inflaton to the gauge field, a time-dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent U(1) gauge kinetic coupling.