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arXiv · 2212.08005

Symmetric Teleparallel Horndeski Gravity

Sebastian Bahamonde·Georg Trenkler·Leonardo G. Trombetta·Masahide Yamaguchi
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Abstract

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. Due to the nature of nonmetricity, there are many more possible ways of constructing second-order theories of gravity. In this regard, up to some assumptions, we find the most general $k$-essence extension of Symmetric Teleparallel Horndeski gravity. We also formulate a novel theory containing higher-order derivatives acting on nonmetricity while still respecting the second-order conditions, which can be recast as an extension of Kinetic Gravity Braiding. We finish our study by presenting the FLRW cosmological equations for our model.

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Sebastian Bahamonde, Georg Trenkler, Leonardo G. Trombetta, Masahide Yamaguchi. 2023-05-09. Symmetric Teleparallel Horndeski Gravity. https://doi.org/10.1103/physrevd.107.104024

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