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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.
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1905
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A. Toporensky, P. Tretyakov, Spin connection and cosmological perturbations in f(T) gravity
1911
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S.-H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis, Cosmological perturbations in f(T) gravity
2011
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B. Li, T.P. Sotiriou, J.D. Barrow, Large-scale Structure in f(T) Gravity
2011
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R. Ferraro, F. Fiorini, Remnant group of local Lorentz transformations in f(T) theories
2015
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Y.-F. Cai, S. Capozziello, M. De Laurentis, E.N. Saridakis, f(T) teleparallel gravity and cosmology
2016
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M. Krššák, E.N. Saridakis, The covariant formulation of f(T) gravity
2016
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A. Golovnev, T. Koivisto, M. Sandstad, On the covariance of teleparallel gravity theories
2017
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C. Bejarano, R. Ferraro, M.J. Guzmán, McVittie solution in f(T) gravity
2017
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A. Golovnev, T. Koivisto, Cosmological perturbations in modified teleparallel gravity models
2018
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H. Abedi, S. Capozziello, R. D’Agostino, O. Luongo, Effective gravitational coupling in modified teleparallel theories
2018
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T. Koivisto, G. Tsimperis, The spectrum of teleparallel gravity
2019
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