标题： 对称平行传输霍恩德斯基 显示英文标题

标题： Symmetric Teleparallel Horndeski

摘要： 霍尔德斯基引力是最一般的标量-张量理论，包含一个标量场，导致度规和标量场的二阶欧拉-拉格朗日场方程，并基于黎曼几何。 在本文中，我们在对称平行几何中提出了霍尔德斯基引力的一个类似版本，该几何假设曲率（一般）和扭力都为零，引力仅与非度规性有关。 我们的设置要求不仅度规和标量场，而且连接的欧拉-拉格朗日方程最多为二阶。 我们发现，该理论可以始终重新表述为黎曼霍尔德斯基理论和纯平行的项之和。 由于非度规性的性质，构造二阶引力理论有更多可能的方式。 在这方面，在一些假设下，我们找到了对称平行霍尔德斯基的最一般的$k$-本质扩展。 我们还提出了一个包含作用于非度规性的高阶导数的新理论，同时仍遵守二阶条件，该理论可以重新表述为动能引力编织的扩展。 我们通过提出我们模型的FLRW宇宙学方程来结束研究。 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. 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.