Seed models in scalar field cosmology

The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is shown that within the framework of this approach, it is possible to obtain a limited class of known inflationary models at early times. It is also shown that on large times the proposed approach leads to the $\Lambda$CDM--model in order to describe the dynamics of the second accelerated expansion of the universe. An interpretation of the considered models is presented as a starting point for constructing verifiable cosmological models based on modified gravity theories.