Focusing conditions for extended teleparallel gravity theories

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.

31 pages, 9 figures, JCAP format, minor changes, matches published version in JCAP

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Cited by in corpus (3)

• Teleparallel Gravity: From Theory to Cosmology
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences