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arXiv · 2009.04353

Focusing conditions for extended teleparallel gravity theories

U. K. Beckering Vinckers·A. de la Cruz-Dombriz·F. J. Maldonado Torralba
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Abstract

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.

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U. K. Beckering Vinckers, A. de la Cruz-Dombriz, F. J. Maldonado Torralba. 2020-09-09. Focusing conditions for extended teleparallel gravity theories. https://doi.org/10.1088/1475-7516/2020/12/020

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