Perturbations in f(T) cosmology and the spin connection

Abstract

In this short paper we explain how the spin connection variables should be introduced into the perturbation theory of the spatially flat cosmology in f(T) gravity with the background tetrad $e^a_{\mu}=a(t)\cdot\delta^a_{\mu}$ and zero background spin connection. In passing, we also correct some small mistakes in our previous work on this subject.