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Then

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2018
Later among the works it cites.
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Later among the works it cites.
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2022

Symmetric Teleparallel Horndeski Gravity

Bahamonde, Sebastian, Trenkler, Georg, Trombetta, Leonardo G. et al.

Understand

Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry.

In this paper, we formulate an analogue version of Horndeski gravity in a symmetric teleparallel geometry which assumes that both the curvature (general) and torsion are vanishing and gravity is only related to nonmetricity.
Our setup requires that the Euler-Lagrange equations for not only metric and scalar field but also connection should be at most second order.
We find that the theory can be always recast as a sum of the Riemannian Horndeski theory and new terms that are purely teleparallel.