Symmetric teleparallel Horndeski gravity
Symmetric teleparallel Horndeski gravity
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DOI：
10.1103/physrevd.107.104024
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发表时间：
2022-12
影响因子：
5
通讯作者：
S. Bahamonde;G. Trenkler;L. G. Trombetta;Masahide Yamaguchi
中科院分区：
文献类型：
--
作者：
S. Bahamonde;G. Trenkler;L. G. Trombetta;Masahide Yamaguchi
Horndeski 引力是最通用的标量张量理论，通过一个标量场导出度量和标量场的二阶欧拉-拉格朗日场方程，它基于黎曼几何。在本文中，我们在对称远平行几何中制定了 Horndeski 引力的模拟版本，假设曲率（一般）和挠率都消失，并且引力仅与非度量相关。我们的设置要求不仅度量场和标量场而且连接的欧拉-拉格朗日方程最多是二阶。我们发现该理论总是可以被重写为黎曼霍恩德斯基理论和纯粹远程平行的新术语的总和。由于非度量性的本质，构建二阶引力理论有更多可能的方法。在这方面，在某些假设下，我们找到了对称远平行霍恩德斯基引力最普遍的$k$-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量性的高阶导数，同时仍然尊重二阶条件，该理论可以被重新定义为动重力编织的扩展。我们通过提出模型的 FLRW 宇宙学方程来完成我们的研究。
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.