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arXiv 2212.08005gr-qcastro-ph.COhep-th
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对称遥平行 Horndeski 引力

Symmetric Teleparallel Horndeski Gravity

Sebastian Bahamonde, Georg Trenkler, Leonardo G. Trombetta, Masahide Yamaguchi

AI总结:

本文在对称遥平行几何中构建了 Horndeski 引力的类似版本,要求度规、标量场和联络的场方程至多为二阶,并找到了最一般的 k-本质扩展及包含高阶导数的新理论,最后给出 FLRW 宇宙学方程。

摘要:

Horndeski 引力是最一般的标量-张量理论,含有一个标量场,导致度规和标量场的欧拉-拉格朗日场方程为二阶,它基于黎曼几何。在本文中,我们在对称遥平行几何中构建了 Horndeski 引力的类似版本,该几何假设曲率(一般的)和挠率均为零,引力仅与非度规性相关。我们的设置要求度规、标量场以及联络的欧拉-拉格朗日方程至多为二阶。我们发现该理论总能被重写为黎曼 Horndeski 理论与纯粹遥平行的新项之和。由于非度规性的本质,构造二阶引力理论的方式更多。在这方面,在一定的假设下,我们找到了对称遥平行 Horndeski 引力的最一般的 k-本质扩展。我们还构建了一个新理论,其中包含作用于非度规性的高阶导数,同时仍满足二阶条件,该理论可被重写为动力学引力编织的扩展。我们最后给出了我们模型的 FLRW 宇宙学方程。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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