# Superpotential method for chiral cosmological models connected with modified gravity

## TL;DR

This paper extends the superpotential method to chiral cosmological models with multiple scalar fields, enabling the construction of exact solutions and new cosmological scenarios, including cyclic universe models and reductions to single-field models.

## Contribution

The paper generalizes the superpotential method for multi-field CCMs, develops solution construction techniques, and introduces new exact solutions and reduction methods for complex cosmological models.

## Key findings

- New classes of exact solutions in two-component CCMs connected with $f(R)$ gravity.
- Reconstruction procedures for kinetic parts with periodic and hyperbolic Hubble parameters.
- Solutions for cyclic universe models with single- and double-field potentials.

## Abstract

We consider the 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 behaviour 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.