# Modeling dark sector in Horndeski gravity at first-order formalism

## TL;DR

This paper explores a cosmological model within Horndeski gravity using first-order formalism, demonstrating that a de Sitter phase can be achieved and the scalar field can mimic dark energy.

## Contribution

It introduces a novel approach to constraining the scalar potential in Horndeski gravity via first-order formalism, enabling dark energy modeling without free potential choices.

## Key findings

- De Sitter phase can be realized at late times.
- Scalar field mimics dark energy behavior.
- No free scalar potential is allowed in the model.

## Abstract

We investigate a cosmological scenario by finding solutions using first-order formalism in the Horndeski gravity that constrains the superpotential and implies that no free choice of scalar potential is allowed. Despite this we show that a de Sitter phase at late-time cosmology can be realized, where the dark energy sector can be identified. The scalar field equation of state tends to the cosmological scenario at present time and allows us to conclude that it can simulate the dark energy in the Horndeski gravity.