Cosmological inflation in supersymmetric conformal theory

The possibility of describing cosmological inflation in the conformal theory of = 1 supergravity is considered. Two cosmological models are investigated. The first model includes one scalar field with a unit conformal weight, which is a complex generalization of the so-called dilaton field used in conformal theories of gravity. Within the framework of this model, a cosmological model with a positive cosmological constant is constructed. The second model describes spontaneous violation of Weyl scale invariance, as a result of which the value of the gravitational constant is established. Within the framework of this model, it is also possible to obtain a cosmological solution describing inflation according to the Hubble law.