Quantum mechanics

Theoretical physics

Curvature

Cosmology

Gravitation

Mathematical physics

Scalar curvature

Surgery

Effective field theory

Classical mechanics

Torsion (gastropod)

Dark energy

Tensor (intrinsic definition)

Physics

Scalar (mathematics)

Mathematics

Geometry

Medicine

General relativity

Physical review. D/Physical review. D.

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. Since this theory is very important in modified gravity, it is then worth studying possible similar theories starting from other frameworks. In this paper, we study the analog of Horndeski's theory in the teleparallel gravity framework where 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 Horndeski contains the standard Horndeski 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 appearance 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.

Can Horndeski theory be recast using teleparallel gravity?