The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most...

We consider chiral cosmological models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the quasi-steady-state (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behavior of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

The problem of determining a representation of the self-interaction potential in the form of a time dependence of the field potential energy which admits the existence of an inflationary regime and th

We study the special class of exact solutions in cosmological models based on generalized scalar-tensor gravity with nonminimal coupling of a scalar field to the Ricci scalar and to the Gauss-Bonnet scalar in a 4D Friedmann universe corresponding to similar ones in GR. The parameters of cosmological perturbations in such models correspond to the case of Einstein gravity with a high precision. As an example of the proposed approach, we obtain the exact solutions for the power-law and exponential power-law inflation.