# Cosmological Evolution and Exact Solutions in a Fourth-order Theory of Gravity

## TL;DR

This paper explores a fourth-order gravity theory with a canonical Lagrangian, analyzing its critical points and demonstrating its capability to model matter-dominated and accelerated universe phases, including de Sitter space, with exact solutions provided.

## Contribution

It introduces a fourth-order gravity model with a canonical Lagrangian and analyzes its cosmological solutions, including matter and accelerated phases, which is a novel approach.

## Key findings

- The theory can describe the matter epoch of the universe.
- It admits two accelerated phases, including a de Sitter universe.
- Exact solutions are obtained for specific models.

## Abstract

A fourth-order theory of gravity is considered which in terms of dynamics has the same degrees of freedom and number of constraints as those of scalar-tensor theories. In addition it admits a canonical point-like Lagrangian description. We study the critical points of the theory and we show that it can describe the matter epoch of the universe and that two accelerated phases can be recovered one of which describes a de Sitter universe. Finally for some models exact solutions are presented.