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Focusing conditions for extended teleparallel gravity theories
Journal of Cosmology and Astroparticle Physics ( IF 6.4 ) Pub Date : 2020-12-09 , DOI: 10.1088/1475-7516/2020/12/020
U.K. Beckering Vinckers 1 , Á. de la Cruz-Dombriz 1 , F.J. Maldonado Torralba 1, 2
Affiliation  

In the context of extended theories of teleparallel gravity $f(T)$ we derive the focusing conditions for a one-parameter dependent congruence of timelike auto-parallels of the Levi-Civita connection. We also consider the $f(T)$ field equations for a general metric tensor before moving on to consider a spatially flat Robertson-Walker space-time. Following this, we study the expansion rate for a one-parameter dependent congruence of timelike auto-parallel curves of the Levi-Civita connection. Given the fact that test particles follow auto-parallels of the Levi-Civita connection, the torsion-free Raychaudhuri equation is used in order to determine the desired focusing conditions. Finally we study the obtained focusing conditions for three $f(T)$ paradigmatic cosmological models and discuss the satisfaction or violation of these conditions. Through this, we find $f(T)$ models that allow for the weak and strong focusing conditions to be satisfied or violated. It is mentioned that this behaviour can also be found in the so-called $f(R)$ and $f(Q)$ theories.

中文翻译:

扩展远平行引力理论的聚焦条件

在远程平行引力的扩展理论 $f(T)$ 的背景下,我们推导出了 Levi-Civita 连接的类时自动平行的单参数相关同余的聚焦条件。在继续考虑空间平坦的 Robertson-Walker 时空之前,我们还考虑了通用度量张量的 $f(T)$ 场方程。在此之后,我们研究了 Levi-Civita 连接的类时自平行曲线的单参数相关同余的扩展率。鉴于测试粒子遵循 Levi-Civita 连接的自动平行,使用无扭转 Raychaudhuri 方程来确定所需的聚焦条件。最后,我们研究了三个 $f(T)$ 范式宇宙学模型的聚焦条件,并讨论了这些条件的满足或违反。通过这个,我们找到了允许满足或违反弱和强聚焦条件的 $f(T)$ 模型。提到这种行为也可以在所谓的 $f(R)$ 和 $f(Q)$ 理论中找到。
更新日期:2020-12-09
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