标题： 对称共线霍恩德斯基本引力 显示英文标题

标题： Symmetric Teleparallel Horndeski Gravity

摘要： 霍尼德斯基本理论是最一般的具有一个标量场的标量-张量理论，它使度规和标量场的欧拉-拉格朗日场方程具有二阶导数，并且基于黎曼几何。 本文中，我们在对称平移几何中制定了霍尼德斯基本理论的类比版本，该几何假设曲率（广义）和挠率都消失，并且引力仅与非度规性有关。 我们的设定要求不仅度规和标量场的欧拉-拉格朗日方程，而且连接的方程也应至多为二阶。 我们发现该理论可以始终改写为黎曼霍尼德斯基理论与新的纯平移项之和。 由于非度规性的性质，有更多可能的方法来构建二阶引力理论。 在此方面，在某些假设下，我们找到了对称平移霍尼德斯基引力的最一般$k$-本质扩展。 我们还制定了一种新颖的理论，其中包含作用于非度规性的高阶导数，同时仍然满足二阶条件，它可以改写为动力学引力编织的扩展。 通过给出我们模型的FLRW宇宙学方程，我们完成了这项研究。 显示英文摘要

摘要： 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.