# The method of generating functions in exact scalar field cosmology

## TL;DR

This paper reviews the generating functions method for constructing exact solutions in scalar field cosmology, discusses the superpotential approach, and proposes a classification linking these methods.

## Contribution

It introduces a classification of generating functions and connects them with the superpotential method, enhancing understanding of solution construction in scalar field cosmology.

## Key findings

- Established a classification scheme for generating functions.
- Linked generating functions with the superpotential method.
- Provided insights into exact solutions in scalar field cosmology.

## Abstract

Exact solutions construction in scalar fields cosmology is of growing interest. In this work we review the results which obtained with the help of one of the most effective method. Namely, the method of generating functions for exact solutions construction in the scalar field cosmology. We also included into debate the superpotential method which may be considered as the bridge to slow roll approximation equations. Basing on the review, we suggested classification for the generating functions and found connection for all of them with the superpotential.