# Can Horndeski Theory be recast using Teleparallel Gravity?

## TL;DR

This paper explores a teleparallel gravity analogue of Horndeski theory, revealing richer phenomenology and potential explanations for dark energy, inflation, and Hubble tension, expanding the landscape of modified gravity models.

## Contribution

It introduces a teleparallel version of Horndeski gravity, encompassing standard Horndeski and past teleparallel theories, with new terms enabling explanations for dark energy and cosmological tensions.

## Key findings

- Contains the standard Horndeski theory as a special case
- Can explain dark energy without a cosmological constant
- Potentially addresses H0 tension and inflation phenomena

## Abstract

Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second order field equations and after the GW170817 it has been severely constrained. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski gravity as a subcase and also contains many modified Teleparallel theories considered in the past, such as $f(T)$ gravity or Teleparallel Dark energy. Thus, due to the appearing of a new term in the Lagrangian, this theory can explain dark energy without a cosmological constant, may describe a crossing of the phantom barrier, explain inflation and also solve the tension for $H_0$, making it a good candidate for a correct modified theory of gravity.