# Exact Inflation in Einstein-Gauss-Bonnet Gravity

## TL;DR

This paper explores exact inflationary solutions in Einstein-Gauss-Bonnet gravity with a scalar field, providing methods to construct such solutions for specific scale factors in a flat universe.

## Contribution

It introduces a novel method for constructing exact inflationary solutions in Einstein-Gauss-Bonnet gravity with a scalar field, based on a special ansatz linking scale factor and coupling.

## Key findings

- Existence of exponential and power-law inflation solutions.
- Development of a method to generate exact solutions for given scale factors.
- Examples of exact inflationary solutions in the Einstein-Gauss-Bonnet framework.

## Abstract

We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are allowable and we found few examples of them. We also proposed the method of the exact inflationary solutions construction for a single scalar field with given scale factor and Gauss-Bonnet coupling term in the spatially flat Friedmann-Robertson-Walker Universe on the basis of connection with standard inflation and using special anzatses. With one special anzats we presented the system of equations in the form which allowed generation of exact solutions (at least in quadratures) of wide class by setting the scale factor.