Modern cosmology is extensively studied by the scientific community in an attempt to answer many issues about the universe. The theoretical basis underlying all this theory is general relativity. However, there are other approaches such as modified theories of gravity that try to solve a series of problems in cosmology, particularly in the study of the early universe, a period known as cosmic inflation. Recently a general theory has been proposed involving scalar and vector fields, opening up the possibility for new studies in cosmology and astrophysics. In this talk we present a model with scalar and vector fields with broken U(1) symmetry non-trivially coupled to gravity and apply it to the study of the early universe.