# Reviving Horndeski Theory using Teleparallel Gravity after GW170817

## TL;DR

This paper proposes a teleparallel gravity framework that allows a more general form of Horndeski theory to satisfy gravitational wave speed constraints, effectively reviving aspects of the original theory.

## Contribution

It introduces a teleparallel gravity approach that restores the coupling functions in Horndeski theory, bypassing previous observational constraints.

## Key findings

- Allows $G_5(,X)$ and $G_4(,X)$ functions without violating GW speed constraints
- Constructs a more general Horndeski theory compatible with GW170817 observations
- Revives the potential of Horndeski gravity within a teleparallel framework

## Abstract

Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to $|c_{g}/c-1|\gtrsim 10^{-15}$. In this Letter we study the tensorial perturbations in a flat cosmological background for an analogue version of Horndenki gravity which is based in Teleparallel Gravity constructed from a flat manifold with a nonvanishing torsion tensor. It is found that in this approach, one can construct a more general Horndeski theory satisfying $c_T=c_g/c=1$ without eliminating the coupling functions $G_5(\phi,X)$ and $G_4(\phi,X)$ that were highly constrained in standard Horndeski theory. Hence, in the Teleparallel approach one is able to restore these terms, creating an interesting way to revive Horndeski gravity.