Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity

TL;DR

This paper investigates the stability of teleparallel Horndeski gravity models, identifying conditions under which these theories avoid ghost and Laplacian instabilities, thus narrowing down physically viable models within this broad class.

Contribution

It provides the first comprehensive analysis of ghost and Laplacian instabilities in teleparallel Horndeski gravity, establishing stability constraints for a wide range of models.

Findings

Many models are found to be free of ghost instabilities.

A large subset of models avoids Laplacian instabilities.

Stability constraints significantly restrict the parameter space of the theories.

Abstract

Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide range of models coming from ghost and Laplacian instabilities. The aim is to limit pathological branches of the theory by fundamental considerations. It is possible to conclude that a very large class of models results physically viable.