By perturbing f(T) gravity around FLRW and Bianchi I spacetimes, the authors find that only the two gravitational-wave polarizations propagate in the gravity sector.
The growth of matter perturbations in the f(T) gravity
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In this paper, we study the growth index of matter density perturbations for the power law model in $f(T)$ gravity. Using the parametrization $\gamma(z)=\gamma_0+\gamma_1 {z\over 1+z}$ for the growth index, which approximates the real evolution of $\gamma(z)$ very well, and the observational data of the growth factor, we find that, at $1\sigma$ confidence level, the power law model in $f(T)$ gravity is consistent with the observations, since the obtained theoretical values of $\gamma_0$ and $\gamma_1$ are in the allowed region.
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$f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
By perturbing f(T) gravity around FLRW and Bianchi I spacetimes, the authors find that only the two gravitational-wave polarizations propagate in the gravity sector.