Ghost and Laplacian instabilities in teleparallel Horndeski gravity

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. Teleparallel gravity is based on the tetrad formalism. This turns out to result in a more general formalism of 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.

Automated summary

Teleparallel geometry provides a theoretical framework where gravitational interaction is mediated by torsion rather than curvature. Teleparallel analogue of Horndeski gravity is an approach within this framework considering scalar-tensor theories. It is a more general formalism than the standard metric one, allowing for a wider range of teleparallel Horndeski gravity models. The article explores constraints on these models in terms of ghost and Laplacian instabilities and finds that a large class of models is physically viable.